Tag Archives: accuracy of forecasts

accuracy of forecasts, business cycle, macroeconomic forecasting

The Business Cycle

The National Bureau of Economic Research (NBER) has a standing committee which designates the start and finish of recessions, or more precisely, the dates of the peaks and troughs of the US business cycle.

And the NBER site maintains a complete record of the US business cycle, dating back to the middle 1800’s, as shown in the following tables.

NBERbsdates

Periods of contraction, from peak to trough, are typically shorter than periods of expansion – or the movement from previous trough to the next peak.

Since World War II, the average length of the business cycle, variously measured from trough to trough or from peak to peak, is more than 5 years.

Focusing on the current situation, we are interested in the length of time from the previous peak of the business cycle in December 2007 to the next peak. The longest peak to peak period was over the prosperity of the 1990’s, and lasted more than 10 years (128 months).

So, it would be unusual if the peak of this current business cycle were much later than 2017-2018.

In terms of predicting turning points, matters are complicated by the fact that, unlike many European countries, the NBER does not define a recession in terms of two consecutive quarters of decline in real GDP.

Rather, a recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales.

But just predicting the onset of two consecutive quarters of decline in real GDP is challenging. Indeed, the record of macroeconomic forecasting is very poor in this regard.

Part of the problem with the concept of a “cycle” in this context is the irregularity of the fluctuations derived by standard filters and methods.

Harvey, for example, applies low band and pass Butterworth filters to US total investment and other macroeconomic series, deriving, at one pont, an investment “cycle” that looks like this.

Invcycle

So almost everything that makes a cycle useful in prediction is missing from this investment cycle. Thus, one cannot conclude that a turning point will occur, when the amplitude of the cycle is reached, since the amplitudes of these quasi-cycles vary considerably. Similarly, the “period” of the cycle is by no means fixed, but is basically stochastic, with a certain variance sometimes expressed as a “hyperparameter.” Only a certain quality of smoothness presents itself, and, of course, is a result of the filtering parameters that are applied.

In my opinion, industry cycles make a certain amount of sense, for particular industries, over particular spans of time. What I mean is that identification of such industry cycles improves predictability of the underlying series – be it sales or inventories or what have you.

The business cycle, on the other hand, is something of a metaphor, or maybe just an evocative phrase.

True, there are periods of economic contraction and periods of expansion.

But the extraction of macroeconomic cycles often does not improve predictability, because the fluctuations so identified are highly irregular from a number of different viewpoints.

I’ve sort of confirmed this is a quantitative sense by applying various cycle-extraction softwares to US real GDP to see whether any product or approach gave a hint that the Great Recession which began in 2008 would (a) occur, and (b) be as dramatic as it was. So far, no go.

And, of course, Ng points out that the Great Recession was fundamentally different than, say, recessions in the 1960’s sand 1970’s in that it was a balance sheet recession.

ARIMA models, macroeconomic forecasting, Uncategorized

Cycles -1

I’d like  to focus on cycles in business and economic forecasting for the next posts.

The Business Cycle

“Cycles” – in connection with business and economic time series – evoke the so-called business cycle.

Immediately after World War II, Burns and Mitchell offered the following characterization –

Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle

Earlier, several types of business and economic cycles were hypothesized, based on their average duration. These included the 3 to 4 year Kitchin inventory investment cycle, a 7 to 11 year Juglar cycle associated with investment in machines, the 15 to 25 year Kuznets cycle, and the controversial Kondratieff cycle of from 48 to 60 years.

Industry Cycles

I have looked at industry cycles relating to movements of sales and prices in semiconductor and computer markets. While patterns may be changing, there is clear evidence of semi-regular pulses of activity in semiconductors and related markets. These stochastic cycles probably are connected with Moore’s Law and the continuing thrust of innovation and new product development.

Methods

Spectral analysis, VAR modeling, and standard autoregressive analysis are tools for developing evidence for time series cycles. STAMP, now part of the Oxmetrics suite of software, fits cycles with time-varying parameters.

Sometimes one hears of estimations in the time domain moving into the frequency domain. Time series, as normally graphed with time on the horizontal axis, are in the “time domain.” This is where VAR and autoregressive models operate. The frequency domain is where we get indications of the periodicity of cycles and semi-cycles in a time series.

Cycles as Artifacts

There is something roughly analogous to spurious correlation in regression analysis in the identification of cyclical phenomena in time series. Eugen Slutsky, a Russian mathematical economist and statistician, wrote a famous “unknown” paper on how moving averages of random numbers can create the illusion of cycles. Thus, if we add or average together elements of a time series in a moving window, it is easy to generate apparently cyclical phenomena. This can be demonstrated with the digits in the irrational number π, for example, since the sequence of digits 1 through 9 in its expansion is roughly random.

Significances

Cycles in business have sort of reassuring effect, it seems to me. And, of course, we are all very used to any number of periodic phenomena, ranging from the alternation of night and day, the phases of the moon, the tides, and the myriad of biological cycles.

As a paradigm, however, they probably used to be more important in business and economic circles, than they are today. There is perhaps one exception, and that is in rapidly changing high tech fields of which IT (information technology) is still in many respects a subcategory.

I’m looking forward to exploring some estimations, putting together some quantitative materials on this.

accuracy of forecasts, Big Data, forecasting research, macroeconomic forecasting

Seasonal Adjustment – A Swirl of Controversies

My reading on procedures followed by the Bureau of Labor Statistics (BLS) and the Bureau of Economic Analysis (BLS) suggests some key US macroeconomic data series are in a profound state of disarray. Never-ending budget cuts to these “non-essential” agencies, since probably the time of Bill Clinton, have taken their toll.

For example, for some years now it has been impossible for independent analysts to verify or replicate real GDP and many other numbers issued by the BEA, since, only SA (seasonally adjusted) series are released, originally supposedly as an “economy measure.” Since estimates of real GDP growth by quarter are charged with political significance in an Election Year, this is a potential problem. And the problem is immediate, since the media naturally will interpret a weak 2nd quarter growth – less than, say, 2.9 percent – as a sign the economy has slipped into recession.

Evidence of Political Pressure on Government Statistical Agencies

John Williams has some fame with his site Shadow Government Statistics. But apart from extreme stances from time to time (“hyperinflation”), he does document the politicization of the BLS Consumer Price Index (CPI).

In a recent white paper called No. 515—PUBLIC COMMENT ON INFLATION MEASUREMENT AND THE CHAINED-CPI (C-CPI), Williams cites Katharine Abraham, former commissioner of the Bureau of Labor Statistics, when she notes,

“Back in the early winter of 1995, Federal Reserve Board Chairman Alan Greenspan testified before the Congress that he thought the CPI substantially overstated the rate of growth in the cost of living. His testimony generated a considerable amount of discussion. Soon afterwards, Speaker of the House Newt Gingrich, at a town meeting in Kennesaw, Georgia, was asked about the CPI and responded by saying, ‘We have a handful of bureaucrats who, all professional economists agree, have an error in their calculations. If they can’t get it right in the next 30 days or so, we zero them out, we transfer the responsibility to either the Federal Reserve or the Treasury and tell them to get it right.’”[v]

Abraham is quoted in newspaper articles as remembering sitting in Republican House Speaker Newt Gingrich’s office:

“ ‘He said to me, If you could see your way clear to doing these things, we might have more money for BLS programs.’ ” [vi]

The “things” in question were to move to quality adjustments for the basket of commodities used to calculate the CPI. The analogue today, of course, is the chained-CPI measure which many suggest is being promoted to slow cost-of-living adjustments in Social Security payments.

Of course, the “real” part in real GDP is linked with the CPI inflation outlook though a process supervised by the BEA.

Seasonal Adjustment Procedures for GDP

Here is a short video by Johnathan H. Wright, a young economist whose Unseasonal Seasonals? is featured in a recent issue of the Brookings Papers on Economic Activity.

Wright’s research is interesting to forecasters, because he concludes that algorithms for seasonally adjusting GDP should be selected based on their predictive performance.

Wright favors state-space models, rather than the moving-average techniques associated with the X-12 seasonal filters that date back to the 1980’s and even the 1960’s.

Given BLS methods of seasonal adjustment, seasonal and cyclical elements are confounded in the SA nonfarm payrolls series, due to sharp drops in employment concentrated in the November 2008 to March 2009 time window.

The upshot – initially this effect pushed reported seasonally adjusted nonfarm payrolls up in the first half of the year and down in the second half of the year, by slightly more than 100,000 in both cases…

One of his prime exhibits compares SA and NSA nonfarm payrolls, showing that,

The regular within-year variation in employment is comparable in magnitude to the effects of the 1990–1991 and 2001 recessions. In monthly change, the average absolute difference between the SA and NSA number is 660,000, which dwarfs the normal month-over-month variation in the SA data.

SEASnonseas

The basic procedure for this data and most releases since 2008-2009 follows what Wright calls the X-12 process.

The X-12 process focuses on certain types of centered moving averages with a fixed weights, based on distance from the central value.

A critical part of the X-12 process involves estimating the seasonal factors by taking weighted moving averages of data in the same period of different years. This is done by taking a symmetric n-term moving average of m-term averages, which is referred to as an n × m seasonal filter. For example, for n = m = 3, the weights are 1/3 on the year in question, 2/9 on the years before and after, and 1/9 on the two years before and after.16 The filter can be a 3 × 1, 3 × 3, 3 × 5, 3 × 9, 3 × 15, or stable filter. The stable filter averages the data in the same period of all available years. The default settings of the X-12…involve using a 3 × 3, 3 × 5, or 3 × 9 seasonal filter, depending on [various criteria]

Obviously, a problem arises at the beginning and at the end of the time series data. A work-around is to use an ARIMA model to extend the time series back and forward in time sufficiently to calculate these centered moving averages.

Wright shows these arbitrary weights and time windows lead to volatile seasonal adjustments, and that, predictively, the BEA and BLS would be better served with a state-space model based on the Kalman filter.

Loopy seasonal adjustment leads to controversy that airs on the web – such as this piece by Zero Hedge from 2012 which highlights the “ficititious” aspect of seasonal adjustments of highly tangible series, such as the number of persons employed –

What is very notable is that in January, absent BLS smoothing calculation, which are nowhere in the labor force, but solely in the mind of a few BLS employees, the real economy lost 2,689,000 jobs, while net of the adjustment, it actually gained 243,000 jobs: a delta of 2,932,000 jobs based solely on statistical assumptions in an excel spreadsheet!

To their credit, Census now documents an X-13ARIMA-SEATS Seasonal Adjustment Program with software incorporating elements of the SEATS procedure originally developed at the Bank of Spain and influenced by the state space models of Andrew Harvey.

Maybe Wright is getting some traction.

What Is The Point of Seasonal Adjustment?

You can’t beat the characterization, apparently from the German Bundesbank, of the purpose and objective of “seasonal adjustment.”

..seasonal adjustment transforms the world we live in into a world where no seasonal and working-day effects occur. In a seasonally adjusted world the temperature is exactly the same in winter as in the summer, there are no holidays, Christmas is abolished, people work every day in the week with the same intensity (no break over the weekend)..

I guess the notion is that, again, if we seasonally adjust and see a change in direction of a time series, why then it probably is a change in trend, rather than from special uses of a certain period.

But I think most of the professional forecasting community is beyond just taking their cue from a single number. It would be better to have the raw or not seasonally adjusted (NSA) series available with every press release, so analysts can apply their own models.

accuracy of forecasts, analyzing seasonal effects, energy forecasting, gasoline price forecasts, long term forecasting, univariate forecast modeling approaches

Analyzing Complex Seasonal Patterns

When time series data are available in frequencies higher than quarterly or monthly, many forecasting programs hit a wall in analyzing seasonal effects.

Researchers from the Australian Monash University published an interesting paper in the Journal of the American Statistical Association (JASA), along with an R program, to handle this situation – what can be called “complex seasonality.”

I’ve updated and modified one of their computations – using weekly, instead of daily, data on US conventional gasoline prices – and find the whole thing pretty intriguing.

tbatschart

If you look at the color codes in the legend below the chart, it’s a little easier to read and understand.

Here’s what I did.

I grabbed the conventional weekly US gasoline prices from FRED. These prices are for “regular” – the plain vanilla choice at the pump. I established a start date of the first week in 2000, after looking the earlier data over. Then, I used tbats(.) in the Hyndman R Forecast package which readers familiar with this site know can be downloaded for use in the open source matrix programming language R.

Then, I established an end date for a time series I call newGP of the first week in 2012, forecasting ahead with the results of applying tbats(.) to the historic data from 2000:1 to 2012:1 where the second number refers to weeks which run from 1 to 52. Note that some data scrubbing is needed to shoehorn the gas price data into 52 weeks on a consistent basis. I averaged “week 53” with the nearest acceptable week (either 52 or 1 in the next year), and then got rid of the week 53’s.

The forecast for 104 weeks is shown by the solid red line in the chart above.

This actually looks promising, as if it might encode some useful information for, say, US transportation agencies.

A draft of the JASA paper is available as a PDF download. It’s called Forecasting time series with complex seasonal patterns using exponential smoothing and in addition to daily US gas prices, analyzes daily electricity demand in Turkey and bank call center data.

I’m only going part of the way to analyzing the gas price data, since I have not taken on daily data yet. But the seasonal pattern identified by tbats(.) from the weekly data is interesting and is shown below.

tbatsgasprice

The weekly frequency may enable us to “get inside” a mid-year wobble in the pattern with some precision. Judging from the out-of-sample performance of the model, this “wobble” can in some cases be accentuated and be quite significant.

Trignometric series fit to the higher frequency data extract the seasonal patterns in tbats(.), which also features other advanced features, such as a capability for estimating ARMA (autoregressive moving average) models for the residuals.

I’m not fully optimizing the estimation, but these results are sufficiently strong to encourage exploring the toggles and switches on the routine.

Another routine which works at this level of aggregation is the stlf(.) routine. This is uses STL decomposition described in some detail in Chapter 36 Patterns Discovery Based on Time-Series Decomposition in a collection of essays on data mining.

Thoughts

Good forecasting software elicits sort of addictive behavior, when initial applications of routines seem promising. How much better can the out-of-sample forecasts be made with optimization of the features of the routine? How well does the routine do when you look at several past periods? There is even the possibility of extracting further information from the residuals through bootstrapping or bagging at some point. I think there is no other way than exhaustive exploration.

The payoff to the forecaster is the amazement of his or her managers, when features of a forecast turn out to be spot-on, prescient, or what have you – and this does happen with good software. An alternative, for example, to the Hyndman R Forecast package is the program STAMP I also am exploring. STAMP has been around for many years with a version running – get this – on DOS, which appears to have had more features than the current Windows incarnation. In any case, I remember getting a “gee whiz” reaction from the executive of a regional bus district once, relating to ridership forecasts. So it’s fun to wring every possible pattern from the data.

accuracy of forecasts, global business forecasts

Seasonal Sales Patterns – Stylized Facts

Seasonal sales patterns in the United States are more or less synchronized with Europe, Japan, China, and, to a lesser extent, the rest of the world.

Here are some stylized facts:

  1. Sales tend to peak at the end of the calendar year. This is the well-known “Christmas effect,” and is a strong enough factor to “cannibalize” demand, to an extent, at the first of the following year.
  2. Sales of final goods tend to be lower – in terms of growth rates and, in some cases, absolutely, in the first calendar quarter of the year.
  3. Supply chain effects, related to pulses of sales of final goods, can be identified for various lines of production depending on production lead times. Semiconductor orders, for example, tend to peak earlier than sales of consumer electronics, which are sharply influenced by the Christmas season.

To validate this picture, let me offer some evidence.

First, consider retail and food service sales data for the US, a benchmark of consumer activity – the recently discussed data downloaded from FRED.

Applying the automatic model selection of the Hyndman R Forecast package, we get a decomposition of this time series into level, trend, and seasonals, as shown in the following diagram.

Rplotrs

The optimal exponential smoothing forecast model is a model with a damped trend and multiplicative seasonals.

If we look at the lower part of this diagram, we see that the seasonal factor for December – which is shown by the major peaks in the curve – is a multiple of more than 1.15. On the other hand, the immediately following month – January – shows a multiple of 0.9. These factors are multiplied into the product of the level and trend to get the sales for December and January. In other words, you can suppose that, roughly speaking, December retail sales will be 15 percent above trend, while January sales will be 90 percent of trend.

And, if you inspect this diagram in the lower panel carefully, you can detect the lull in late summer and fall in retail sales.

With “just-in-time” inventories and lean production models, actual production activity closely tracks these patterns in final demand – although it does take some lead time to produce stuff.

These stylized facts have not changed in their outlines since the ground-breaking research of Jeffrey Miron in the the late 1980’s. Miron refers to a worldwide seasonal cycle in aggregate economic activity whose major features are a fourth quarter boom in output.., a third quarter trough in manufacturing production, and a first quarter trough in all economic activity.

The Effects of Different Calendars – the Chinese New Year and Ramadan

The Gregorian calendar has achieved worldwide authority, and almost every country follows on the conventions of counting the year (currently 2014).

The Chinese calendar, however, is still important for determining the timing of festivals for Chinese communities around the world, and, especially, in China.

GRAPHICS TEMPLATE 2006

Similarly, the Islamic calendar governs the timing of important ritual periods and religious festivals – such as the month of Ramadan, which falls in June and July in 2014.

Because these festival periods overlap with multiple Gregorian months, there can be significant localized impacts on estimates of seasonal variation of economic activity.

Taiwanese researchers looking at this issue find significant holiday effects, related the fact that,

The three most important Chinese holidays, Chinese New Year, the Dragon-boat Festival, and Mid-Autumn Holiday have dates determined by a lunar calendar and move between two solar months. Consumption, production, and other economic behavior in countries with large Chinese population including Taiwan are strongly affected by these holidays. For example, production accelerates before lunar new year, almost completely stops during the holidays and gradually rises to an average level after the holidays.

Similarly, researchers in Pakistan consider the impacts of the Islamic festivals on standard macroeconomic and financial time series.

accuracy of forecasts, identifying seasonal effects, macroeconomic forecasting, sales forecasting, time series forecasting

Seasonal Variation

Evaluating and predicting seasonal variation is a core competence of forecasting, dating back to the 1920’s or earlier. It’s essential to effective business decisions. For example, as the fiscal year unfolds, the question is “how are we doing?” Will budget forecasts come in on target, or will more (or fewer) resources be required? Should added resources be allocated to Division X and taken away from Division Y? To answer such questions, you need a within-year forecast model, which in most organizations involves quarterly or monthly seasonal components or factors.

Seasonal adjustment, on the other hand, is more mysterious. The purpose is more interpretive. Thus, when the Bureau of Labor Statistics (BLS) or Bureau of Economic Analysis (BEA) announce employment or other macroeconomic numbers, they usually try to take out special effects (the “Christmas effect”) that purportedly might mislead readers of the Press Release. Thus, the series we hear about typically are “seasonally adjusted.”

You can probably sense my bias. I almost always prefer data that is not seasonally adjusted in developing forecasting models. I just don’t know what magic some agency statistician has performed on a series – whether artifacts have been introduced, and so forth.

On the other hand, I take the methods of identifying seasonal variation quite seriously. These range from Buys-Ballot tables and seasonal dummy variables to methods based on moving averages, trigonometric series (Fourier analysis), and maximum likelihood estimation.

Identifying seasonal variation can be fairly involved mathematically.

But there are some simple reality tests.

Take this US retail and food service sales series, for example.

retailfs

Here you see the highly regular seasonal movement around a trend which, at times, is almost straight-line.

Are these additive or multiplicative seasonal effects? If we separate out the trend and the seasonal effects, do we add them or are the seasonal effects “factors” which multiply into the level for a month?

Well, for starters, we can re-arrange this time series into a kind of Buys-Ballot table. Here I only show the last two years.

BBTab

The point is that we look at the differences between the monthly values in a year and the average for that year. Also, we calculate the ratios of each month to the annual total.

The issue is which of these numbers is most stable over the data period, which extends back to 1992 (click to enlarge).

additive

mult

Now here Series N relates to the Nth month, e.g. Series 12 = December.

It seems pretty clear that the multiplicative factors are more stable than the additive components in two senses. First, some additive components have a more pronounced trend; secondly, the variability of the additive components around this trend is greater.

This gives you a taste of some quick methods to evaluate aspects of seasonality.

Of course, there can be added complexities. What if you have daily data, or suppose there are other recurrent relationships. Then, trig series may be your best bet.

What if you only have two, three, or four years of data? Well, this interesting problem is frequently encountered in practical applications.

I’m trying to sort this material into posts for this coming week, along with stuff on controversies that swirl around the seasonal adjustment of macro time series, such as employment and real GDP.

Stay tuned.

Top image from http://www.livescience.com/25202-seasons.html

accuracy of forecasts, analytical software, automatic forecasting software, exponential smoothing

Exponential Smoothing – Black Box Examples

The reason why most people would be interested in and concerned with exponential smoothing (ES) is that it is an effective forecasting technique.

So, with that in mind, I want to discuss two automatic forecasting programs – Forecast Pro and Hyndman’s Forecast program for R – applied to a monthly time series for public construction spending in the US. I do this more or less “black box” in that I am not spending a lot of time on the underlying theory – which is basically a state space model framework – but focus on the process of getting the forecasts and their comparison.

I am testing these programs with a backcasting exercise. Thus, the data for this time series, available from FRED begin January 1993 and extend through May 2014. However, I only use data up to May 2010 to develop forecasting models with these programs. Then, I can compare the forecasts from the models with actual values. So instead of forecasting, you might say I am backcasting. Sometimes this is also called retrodiction, in contrast to prediction.

FREDCS

My plan is to feed both programs data up to and including May 2010, in order to forecast values for the next 24 months.

Forecast Pro

Data input is the first step, and this can be accomplished with Forecast Pro by means of an Excel spreadsheet. There are requirements for how you lay out the data. Basically, the first column, below the first six rows, can contain dates. The first time series is placed in the second column, after noting its name and description, the starting year, starting period (month, quarter, etc), periods per year, and any information on cycles. Then, of course, you store the spreadsheet in a directory where the program can pick it up – but all that is covered in the Forecast Pro manual.

Here’s what the program panel looks like, after you trigger the automatic forecasting procedure (click to enlarge).

FPro

So basically you see a graph of the historic data you are feeding into the program. If you look down to Model Details you will see that expert selection picked a multiplicative Winters linear trend, multiplicative seasonality model. The estimated parameters are then given.

Above this, under Expert Analysis, the screen tells you that it looked at both Box-Jenkins (ARIMA) and ES models, picking the ES model based on out-of-sample tests.

Further down on this screen (not shown), the program lists the forecasts, which are graphed with confidence intervals above (shown).

I’ll discuss these forecasts, but first let me say a few words about the Hyndman R Forecast package analysis.

The Hyndman R Forecast Package

R is very big in some of the enterprise IT outfits. I have friends, for example, who view it as essential, and who have helped me recently come up to speed, to an extent, in using it.

After some fumbling around, I settled on running my R programs in R Studio. There is something called the Comprehensive R Archive Network (CRAN) with important open source R programs. Hyndman et al have their Forecast program listed there, and it pops up in R Studio, which is hugely convenient.

Again, there is an issue of data input. In this case, correctly positioning a csv spreadsheet file works well.

The R code I used to generate ES forecasts is as follows:

R

Note I screw up the spelling of ExponentialSmooth in naming the subdirectory. Oh well.

So after you import the csv file with the read command, you convert it to a time series format. Then, you can apply the operation ets(.) to the time series file, producing the parameters of the optimal ES model, based on comparisons of Akaike information criteria from the maximum likelihood estimations used to calculate the parameters of all the models.

Forecast selects ETS(M,Ad,M) as the optimal model. This indicates an additive trend is used, but is damped, and that the seasonal effects are multiplicative – more or less as in the Forecast Pro analysis.

The Forecasts

I called for 24 months of forecasts from both programs.

Here is a table comparing the forecasts from both packages with the actual values of this public construction time series.

TableFPH

The Hyndman et al R Forecast package produces significantly lower Mean Absolute Percentage Error (MAPE) than Forecast Pro in these forecasts – 2.9% compared with 4.9%.

Here is a chart comparing the absolute percent error by month over the forecast horizon.

compRFP

Conclusions

This particular example is a case of random selection. I really have not run other forecasts with this data and these two models, except for actual future projections. So it’s interesting that an explicitly damped linear trend applied to these data generates a superior forecast to whatever it is that Forecast Pro does.

But readers should be aware that, in many instances, Forecast Pro can slightly outperform the R Forecast program, as Hyndman and coauthors document in a critical paper on this automatic forecasting setup in R.

However, the performance of the two programs is very similar.

In general, I would suggest that non-mathematical users, or folks not used to developing computer programs, stick with Forecast Pro, probably getting the company or organization you work for to pony up several hundred to several thousand dollars to get what you need for the scale of the forecasting problem at hand. Incidentally, I should be getting commissions for boosting this program, as often as I do, but I have no connection with the company.

For more mathematically sophisticated users, I strongly recommend getting up to speed on the R Forecast package and other R packages.

Both would be nice to use together. The R programs can support an interesting research effort, doing all sorts of clever things like fitting splines to the data, boosting, and bagging. Forecast Pro on the other hand is great if you have to produce a large number of forecasts and do not have time to dwell too much on the details of each series.

accuracy of forecasts, analytical software, exponential smoothing forecasts

Exponential Smoothing – I

As I wrote recently, most business forecasting assignments are relatively simple. You collect the data (often the most challenging part), and plug this data into an automatic forecasting program. The program probably applies some type of exponential smoothing (ES) to produce forecasts for a horizon of a few periods ahead, and, bam, there you have it. The rest is presentation, developing the “story” and so forth.

So what about this exponential smoothing? What’s basically involved? What are the differences between exponential smoothing and the other primary univariate forecasting technique – ARIMA or Box-Jenkins modeling? What are these automatic forecasting programs, and which ones are best?

All good questions, and, if you are interested or involved in forecasting, the answers are good to rehearse from time to time.

Level, Trend, Seasonality – Components of Time Series

Exponential smoothing originated with the work of Brown and Holt for the US Navy (see the discussion in Gardiner). The perspective was not theoretical, but applied.

Nevertheless, there is an intuitive aspect to exponential smoothing (ES). That has to do with the decomposition of time series into components – such as level, trend, and seasonal effects.

So, applying the algorithms of ES to some time series Xt t=1,2,…,n, we extract estimates of the level Lt, trend Tt, and seasonal component, St, so that at any time t, we can express Xt as

Xt = Lt + Tt + St

This would be an additive model.

It’s also possible that the time series Xt could be multiplicative, as in

Xt = LtTtSt

By way of example, consider the following time series for public construction spending in the US, obtained from FRED (Federal Reserve Economic Data).

PCS

Now if you look closely, it’s clear there are strongly delineated seasonal effects. Furthermore, these seasonal variations appear to fluctuate more or less in proportion to the annual levels of the series. Thus, the variation is considerably more over a year, when spending is at a $25 billion level, than it does at a $10 billion level.

And the fact that these levels are different, and the series does not simply oscillate around a single level, indicates that there is probably a meaningful trend component to this time series.

Automatic Forecasting Programs

These are the considerations that you take into account in building an exponential smoothing model.

Now it is possible to create ES models within the framework of a spreadsheet. Thus, ES models have smoothing parameters which can be set by minimizing a squared sum of forecast errors over historic data. In Microsoft’s Excel, you can use Solver to do this, once you set up the recursion equations for level, trend, and seasonal components or effects.

In coming posts, I want to show how this can be done for a simple example.

But really, setting up spreadsheets to estimate exponential smoothing models can be laborious, since you need a separate set of computations for every possible model. In addition to the additive and purely multiplicative models shown above, for example, there can be hybrid cases – multiplicative seasonality but additive trend, and so forth.

So it’s a good idea to equip yourself with one of the several, good automatic forecasting programs out there to speed model identification and evaluation.

I will have reference to two such automatic forecasting programs in coming posts – Forecast Pro and Rob Hyndman’s Forecast package in R. I’ll make comparisons between these programs. A demo version of Forecast Pro is available for download for free, but it is a commercial package with various options at various price steps. Hyndman’s R forecasting package, on the other hand, is open source software and free, as is the R platform. While this sounds like an unbeatable advantage, there always are questions of bugs and performance – which in this case seem to be to be resolved for reasons we can discuss.

What’s The Big Deal?

Finally, the reason why ES forecasting is so widely applied is that, in many cases, it produces forecasts which are of comparable or superior accuracy to other univariate forecasting approaches.

ES has performed well, for example, in international forecasting competitions, including the widely-publicized M-competitions.

There also is a link between exponential smoothing and the Kalman filter. So ES is in a sense an adaptive forecasting approach. For example, ES weights more recent observations more heavily than observations more distant in the past, unlike a regression trend model.

Finally, recent research has provided statistical pedigree to exponential smoothing, rescuing it in a sense from consignment to “a purely ad hoc” approach. Thus, there is a direct link between time series that embody a random walk or random walk with drift and exponential smoothing.

accuracy of forecasts, business cycle, business trends, macroeconomic forecasting

Prospects for the 2nd Quarter 2014 and the Rest of the Year

Well, it’s the first day of the 3rd quarter 2014, and time to make an assessment of what happened in Q2 and also what is likely to transpire the rest of the year.

The Big Write-Down

Of course, the 1st quarter 2014 numbers were surprisingly negative – and almost no one saw that coming. Last Wednesday (June 25) the Bureau of Economic Analysis (BEA) revised last estimates of 1st quarter real GDP down a -2.9 percent decrease on a quarter-by-quarter basis.

The Accelerating Growth Meme

Somehow media pundits and the usual ranks of celebrity forecasters seem heavily invested in the “accelerating growth” meme in 2014.

Thus, in mid-June Mark Zandi of Moody’s tries to back up Moody’s Analytics U.S. Macro Forecast calling for accelerating growth the rest of the year, writing,

The economy’s strength is increasingly evident in the job market. Payroll employment rose to a new high in May as the U.S. finally replaced all of the 8.7 million jobs lost during the recession, and job growth has accelerated above 200,000 per month since the start of the year. The pace of job creation is almost double that needed to reduce unemployment, even with typical labor force gains. More of the new positions are also better paying than was the case earlier in the recovery.

After the BEA released its write-down numbers June 25, the Canadian Globe and Mail put a happy face on everything, writing that The US Economy is Back on Track since,

Hiring, retail sales, new-home construction and consumer confidence all rebounded smartly this spring. A separate government report Wednesday showed inventories for non-defense durable goods jumped 1 per cent in May after a 0.4-per-cent increase the previous month.

Forecasts for the Year Being Cut-Back

On the other hand, the International Monetary Fund (IMF) cut its forecast for US growth,

In its annual review of the U.S. economy, the IMF cut its forecast for U.S. economic growth this year by 0.8 percentage point to 2%, citing a harsh winter, a struggling housing market and weak international demand for the country’s products.

Some Specifics

The first thing to understand in this context is that employment is usually a lagging indicator of the business cycle. Ahead of the Curve makes this point dramatically with the following chart.

employment

The chart shows employment change and growth lag changes in the business cycle. Thus, note that the green line peaks after growth in personal consumption expenditures in almost every case, where these growth rates are calculated on a year-over-year basis.

So Zandi’s defense of the Moody’s Analytics accelerating growth forecast for the rest of 2014 has to be taken with a grain of salt.

It really depends on other things – whether for example, retail sales are moving forward, what’s happening in the housing market (to new-home construction and other variables), also to inventories and durable goods spending. Also have exports rebounded, and imports (a subtraction from GDP) been reined in?

Retail Sales

If there is going to be accelerating economic growth, consumer demand, which certainly includes retail sales, has to improve dramatically.

However, the picture is mixed with significant rebound in sales in April, but lower-than-expected retail sales growth in May.

Bloomberg’s June take on this is in an article Cooling Sales Curb Optimism on U.S. Growth Rebound: Economy.

The US Census report estimates U.S. retail and food services sales for May, adjusted for seasonal variation and holiday and trading-day differences, but not for price changes, were $437.6 billion, an increase of 0.3 percent (±0.5)* from the previous month.

Durable Goods Spending

In the Advance Report on Durable Goods Manufacturers’ Shipments, Inventories and Orders May 2014 we learn that,

New orders for manufactured durable goods in May decreased $2.4 billion or 1.0 percent to $238.0 billion, the U.S. Census Bureau announced today.

On the other hand,

Shipments of manufactured durable goods in May, up four consecutive months, increased $0.6 billion or 0.3 percent to $238.6 billion

Of course, shipments are a lagging indicator of the business cycle.

Finally, inventories are surging –

Inventories of manufactured durable goods in May, up thirteen of the last fourteen months, increased $3.8 billion or 1.0 percent to $397.8 billion. This was at the highest level since the series was first published on a NAICS basis and followed a 0.3 percent April increase.

Inventory accumulation is a coincident indicator (in a negative sense) of the business cycle, according to NBER documents.

New Home Construction

From the Joint Release U.S. Department of Housing and Urban Development,

Privately-owned housing units authorized by building permits in May were at a seasonally adjusted annual rate of 991,000. This is 6.4 percent (±0.8%) below the revised April rate of 1,059,000 and is 1.9 percent (±1.4%) below the May 2013 estimate of 1,010,000…

Privately-owned housing starts in May were at a seasonally adjusted annual rate of 1,001,000. This is 6.5 percent (±10.2%)* below the

revised April estimate of 1,071,000, but is 9.4 percent (±11.0%)* above the May 2013 rate of 915,000.

Single-family housing starts in May were at a rate of 625,000; this is 5.9 percent (±12.7%)* below the revised April figure of 664,000.

No sign of a rebound in new home construction in these numbers.

Exports and Imports

The latest BEA report estimates,

April exports were $0.3 billion less than March exports of $193.7 billion. April imports were $2.7 billion more than March imports of $237.8 billion…

Here is a several month perspective.

XM

Essentially, the BEA trade numbers suggest the trade balance deteriorated March to April with a sharp uptick in imports and a slight drop in exports.

Summary

Well, it’s not a clear picture. The economy is teetering on the edge of a downturn, which it may still escape.

Clearly, real growth in Q2 has to be at least 2.9 percent in order to counterbalance the drop in Q1, or else the first half of 2014 will show a net decrease.

CNN offers this with an accompanying video –

Goldman Sachs economists trimmed second quarter tracking GDP to 3.5 percent from 4.1 percent, and Barclays economists said tracking GDP for the second quarter fell to 2.9 percent from 4 percent. At a pace below 3 percent, the economy could show contraction for the first half due to the steep first quarter decline of 2.9 percent.

top picture http://www.bbc.com/news/magazine-24045598

accuracy of forecasts, business trends, forecasting turning points, global business forecasts, predicting recessions

Surprising Revision of First Quarter GDP

I showed a relative this blog a couple of days ago, and, wanting “something spicy,” I pulled up The Record of Failure to Predict Recessions is Virtually Unblemished. The lead picture, as for this post, is Peter Sellers in his role as “Chauncey Gardiner” in Being There. Sellers played a simpleton mistaken for a savant, who would say things that everyone thought was brilliant, such as “There will be growth in the Spring.”

Well, last Wednesday, the US Bureau of Economic Analysis released a third revision of its estimate of the 1st quarter 2014 real GDP growth – down from an initial estimate of a positive .1 percent to -2.9 percent growth at an annual rate.

The BEA News Release says,

Real gross domestic product — the output of goods and services produced by labor and property located in the United States — decreased at an annual rate of 2.9 percent in the first quarter of 2014 according to the “third” estimate released by the Bureau of Economic Analysis….

The decrease in real GDP in the first quarter primarily reflected negative contributions from private inventory investment, exports, state and local government spending, nonresidential fixed investment, and residential fixed investment that were partly offset by a positive contribution from PCE. Imports, which are a subtraction in the calculation of GDP, increased.

Looking at this graph of quarterly real GDP growth rates for the past several years, it’s clear that a -2.9 percent quarter-over-quarter change is a significant size.

usgdpchartcustom

Again, macroeconomic forecasters were caught off guard.

In February of this year, the Survey of Professional Forecasters released its 1st Quarter 2014 consensus forecasts with numbers like –

SPF

Some SPF participants do predict 2014 overall will be a year of recession, as the following chart shows, but they are a tiny minority.

spfrange

A downward revision of almost 3 percentage points on the part of the BEA and almost 5 percent change for the median SPF forecast is poor performance indeed.

One hears things sped up in Q2, but on what basis I do not really know – and I am thinking of tracking key markets in future posts, such as housing, consumer spending, and so forth.

My feeling is that the quandary of the Fed – its desperate need to wind down asset purchases and restore interest rates to historic levels –creates an environment for a kind of “happy talk.”

Here’s some history on the real GDP.

USGDPnew