Category Archives: financial forecasting

Daily High and Low Stock Prices – Falling Knives

The mathematics of random walks form the logical underpinning for the dynamics of prices in stock, currency, futures, and commodity markets.

Once you accept this, what is really interesting is to consider departures from random walk movements of prices. Such distortions can signal underlying biases brought to the table by investors and others with influence in these markets.

“Falling knives” may be an example.

A good discussion is presented in Falling Knives: Do Stocks Really Drop 3 Times Faster Than They Rise?

This article in Seeking Alpha is more or less organized around the following chart.


The authors argue this classic chart is really the result of a “Black Swan” event – namely the Great Recession of 2008-2009. Outside of unusual deviations, however, they try to show that “the rate of rallies and pullbacks are approximately equal.”

I’ve been exploring related issues and presently am confident that there are systematic differences in the volatility of high and low prices over a range of time periods.

This seems odd to say, since high and low prices exist within the continuum of prices, their only distinguishing feature being that they are extreme values over the relevant interval – a trading day or collection of trading days.

However, the variance or standard deviation of daily percent changes or rates of change of high and low prices are systematically different for high and low prices in many examples I have seen.

Consider, for example, rates of change of daily high and low prices for the SPY exchange traded fund (ETF) – the security charted in the preceding graph.


This chart shows the standard deviation of daily rates of change of high and low prices for the SPY over rolling annual time windows.

This evidence suggests higher volatility for daily growth or rates of change of low prices is more than something linked just with “Black Swan events.”

Thus, while the largest differences between standard deviations occur in late 2008 through 2009 – precisely the period of the financial crisis – in 2011 and 2012, as well as recently, we see the variance of daily rates of change of low prices significantly higher than those for high prices.

The following chart shows the distribution of these standard deviations of rates of change of daily high and low prices.


You can see the distribution of the daily growth rates for low prices – the blue line – is fatter in a certain sense, with more instances of somewhat greater standard deviations than the daily growth rates for high prices. As a consequence, too, the distribution of the daily growth rates of low prices shows less concentration near the modal value, which is sharply peaked for both curves.

These are not Gaussian or normal distributions, of course. And I find it interesting that the finance literature, despite decades of recognition of these shapes, does not appear to have a consensus on exactly what types of distributions these are. So I am not going to jump in with my two bits worth, although I’ve long thought that these resemble Laplace Distributions.

In any case, what we have here is quite peculiar, and can be replicated for most of the top 100 ETF’s by market capitalization. The standard deviation of rates of change of current low price to previous low prices generally exceeds the standard deviation of rates of change of high prices, similarly computed.

Some of this might be arithmetic, since by definition high prices are greater numerically than low prices, and we are computing rates of change.

However, it’s easy to dispel the idea that this could account for the types of effects seen with SPY and other securities. You can simulate a random walk, for example, and in thousands of replications with positive prices essentially lose any arithmetic effect of this type in noise.

I believe there is more to this, also.

For example, I find evidence that movements of low prices lead movements of high prices over some time frames.

Investor psychology is probably the most likely explanation, although today we have to take into account the “psychology” of robot trading algorithms. Presumeably, these reflect, in some measure, the predispositions of their human creators.

It’s kind of a puzzle.

Top image from SGS Swinger BlogSpot

The Apostle of Negative Interest Rates

Miles Kimball is a Professor at the University of Michigan, and a vocal and prolific proponent of negative interest rates. His Confessions of a Supply-Side Liberal is peppered with posts on the benefits of negative interest rates.

March 2 Even Central Bankers Need Lessons on the Transmission Mechanism for Negative Interest Rates, after words of adoration, takes the Governor of the Bank of England (Mark Carney) to task. Carney’s problem? Carney wrote recently that unless regular households face negative interest rates in their deposit accounts.. negative interest rates only work through the exchange rate channel, which is zero-sum from a global point of view.

Kimball’s argument is a little esoteric, but promotes three ideas.

First, negative interest rates central bank charge member banks on reserves should be passed onto commercial and consumer customers with larger accounts – perhaps with an exemption for smaller checking and savings accounts with, say, less than $1000.

Second, moving toward electronic money in all transactions makes administration of negative interest rates easier and more effective. In that regard, it may be necessary to tax transactions conducted in paper money, if a negative interest rate regime is in force.

Third, impacts on bank profits can be mitigated by providing subsidies to banks in the event the central bank moved into negative interest rate territory.

Fundamentally, Kimball’s view is that.. monetary policy–and full-scale negative interest rate policy in particular–is the primary answer to the problem of insufficient aggregate demand. No need to set inflation targets above zero in order to get the economy moving. Just implement sufficiently negative interest rates and things will rebound quickly.

Kimball’s vulnerability is high mathematical excellence coupled with a casual attitude toward details of actual economic institutions and arrangements.

For example, in his Carney post,  Kimball offers this rather tortured prose under the heading -“Why Wealth Effects Would Be Zero With a Representative Household” –

It is worth clarifying why the wealth effects from interest rate changes would have to be zero if everyone were identical [sic, emphasis mine]. In aggregate, the material balance condition ensures that flow of payments from human and physical capital have not only the same present value but the same time path and stochastic pattern as consumption. Thus–apart from any expansion of the production of the economy as a whole as a result of the change in monetary policy–any effect of interest rate changes on the present value of society’s assets overall is cancelled out by the effect of interest rate changes on the present value of the planned path and pattern of consumption. Of course, what is actually done will be affected by the change in interest rates, but the envelope theorem says that the wealth effects can be calculated based on flow of payments and consumption flows that were planned initially.

That’s in case you worried a regime of -2 percent negative interest rates – which Kimball endorses to bring a speedy end to economic stagnation – could collapse the life insurance industry or wipe out pension funds.

And this paragraph is troubling from another standpoint, since Kimball believes negative interest rates or “monetary policy” can trigger “expansion of the production of the economy as a whole.” So what about those wealth effects?

Indeed, later in the Carney post he writes,

..for any central bank willing to go off the paper standard, there is no limit to how low interest rates can go other than the danger of overheating the economy with too strong an economic recovery. If starting from current conditions, any country can maintain interest rates at -7% or lower for two years without overheating its economy, then I am wrong about the power of negative interest rates. But in fact, I think it will not take that much. -2% would do a great deal of good for the eurozone or Japan, and -4% for a year and a half would probably be enough to do the trick of providing more than enough aggregate demand.

At the end of the Carney post, Kimball links to a list of his and other writings on negative interest rates called How and Why to Eliminate the Zero Lower Bound: A Reader’s Guide. Worth bookmarking.

Here’s a YouTube video.

Although not completely fair, I have to say all this reminds me of a widely-quoted passage from Keynes’ General Theory –

“Practical men who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back”

Of course, the policy issue behind the spreading adoption of negative interest rates is that the central banks of the world are, in many countries, at the zero bound already. Thus, unless central banks can move into negative interest rate territory, governments are more or less “out of ammunition” when it comes to combatting the next recession – assuming, of course, that political alignments currently favoring austerity over infrastructure investment and so forth, are still in control.

The problem I have might be posed as one of “complexity theory.”

I myself have spent hours pouring over optimal control models of consumption  and dynamic general equilibrium. This stuff is so rarified and intellectually challenging, really, that it produces a mindset that suggests mastery of Portryagin’s maximum principle in a multi-equation setup means you have something relevant to say about real economic affairs. In fact, this may be doubtful, especially when the linkages between organizations are so complex, especially dynamically.

The problem, indeed, may be institutional but from a different angle. Economics departments in universities have, as their main consumer, business school students. So economists have to offer something different.

One would hope machine learning, Big Data, and the new predictive analytics, framed along the lines outlined by Hal Varian and others, could provide an alternative paradigm for economists – possibly rescuing them from reliance on adjusting one number in equations that are stripped of the real, concrete details of economic linkages.

The Interest Rate Conundrum

It’s time to invoke the parable of the fox and the hedgehog. You know – the hedgehog knows one thing, sees the world through the lens of a single commanding idea, while the fox knows many things, entertains diverse, even conflicting points of view.

This is apropos of my reaction to David Stockman’s The Fed’s Painted Itself Into The Most Dangerous Corner In History—–Why There Will Soon Be A Riot In The Casino.

Stockman, former Director of Office of Management and Budget under President Ronald Reagan who later launched into a volatile career in high finance (See currently lends his name to and writes for a spicy website called Contra Corner.

Stockman’s “Why There Will Soon Be a Riot in The Casino” pivots on an Op Ed by Lawrence Summers (Preparing for the next recession) as well as the following somewhat incredible chart, apparently developed from IMF data by Contra Corner researchers.


The storyline is that planetary production fell in current dollar terms in 2015. This isn’t because physical output or hours in service dropped, but because of the precipitous drop in commodity prices and the general pattern of deflation.

All this is apropos of the Fed’s coming decision to raise the federal funds rate from the zero bound (really from about 0.25 percent).

The logic is unassailable. As Summers (former US Treasury Secretary, former President of Harvard, and Professor of Economics at Harvard) writes –

U.S. and international experience suggests that once a recovery is mature, the odds that it will end within two years are about half and that it will end in less than three years are over two-thirds. Because normal growth is now below 2 percent rather than near 3 percent, as has been the case historically, the risk may even be greater now. While the risk of recession may seem remote given recent growth, it bears emphasizing that since World War II, no postwar recession has been predicted a year in advance by the Fed, the White House or the consensus forecast.


Historical experience suggests that when recession comes it is necessary to cut interest rates by more than 300 basis points. I agree with the market that the Fed likely will not be able to raise rates by 100 basis points a year without threatening to undermine the recovery. But even if this were possible, the chances are very high that recession will come before there is room to cut rates by enough to offset it. The knowledge that this is the case must surely reduce confidence and inhibit demand.

So let me rephrase this, to underline the points.

  1. Every business recovery has a finite length
  2. The current business recovery has gone on longer than most and probably will end within two or three years
  3. The US Federal Reserve, therefore, has a limited time in which to restore the federal funds rate to something like its historically “normal” levels
  4. But this means a rapid acceleration of interest rates over the next two to three years, something which almost inevitably will speed the onset of a business downturn and which could have alarming global implications
  5. Thus, the Fed probably will not be able to restore the federal funds rate – actually the only rate they directly control – to historically normal values
  6. Therefore, Fed tools to combat the next recession will be severely constrained.
  7. Given these facts and suppositions, secondary speculative/financial and other responses can arise which themselves can become major developments to deal with.

Header pic of fox and hedgehog from

Coming Attractions

Well, I have been doing a deep dive into financial modeling, but I want to get back to blogging more often. It gets in your blood, and really helps explore complex ideas.

So- one coming attraction here is going to be deeper discussion of the fractal market hypothesis.

Ladislav Kristoufek writes in a fascinating analysis (Fractal Markets Hypothesis and the Global Financial Crisis:Scaling, Investment Horizons and Liquidity) that,

“ is known that capital markets comprise of various investors with very different investment horizons { from algorithmically-based market makers with the investment horizon of fractions of a second, through noise traders with the horizon of several minutes, technical traders with the horizons of days and weeks, and fundamental analysts with the monthly horizons to pension funds with the horizons of several years. For each of these groups, the information has different value and is treated variously. Moreover, each group has its own trading rules and strategies, while for one group the information can mean severe losses, for the other, it can be taken a profitable opportunity.”

The mathematician and discoverer of fractals Mandelbrot and investor Peters started the ball rolling, but the idea maybe seemed like a fad of the 1980’s and 1990s.

But, more and more,  new work in this area (as well as my personal research) points to the fact that the fractal market hypothesis is vitally important.

Forget chaos theory, but do notice the power laws.

The latest  fractal market research is rich in mathematics – especially wavelets, which figure in forecasting, but which I have not spent much time discussing here.

There is some beautiful stuff produced in connection with wavelet analysis.

For example, here is a construction from a wavelet analysis of the NASDAQ from another paper by Kristoufek


The idea is that around 2008, for example, investing horizons collapsed, with long term traders exiting and trading becoming more and more short term. This is associated with problems of liquidity – a concept in the fractal market hypothesis, but almost completely absent from many versions of the so-called “efficient market hypothesis.”

Now, maybe like some physicists, I am open to the discovery of deep keys to phenomena which open doors of interpretation across broad areas of life.

Another coming attraction will be further discussion of forward information on turning points in markets and the business cycle generally.

The current economic expansion is growing long in tooth, pushing towards the upper historically observed lengths of business expansions in the United States.

The basic facts are there for anyone to notice, and almost sound like a litany of complaints about how the last crisis in 2008-2009 was mishandled. But China is decelerating, and the emerging economies do not seem positioned to make up the global growth gap, as in 2008-2009. Interest rates still bounce along the zero bound. With signs of deteriorating markets and employment conditions, the Fed may never find the right time to raise short term rates – or if they plunge ahead will garner virulent outcry. Financial institutions are even larger and more concentrated now than before 2008, so “too big to fail” can be a future theme again.

What is the best panel of financial and macroeconomic data to watch the developments in the business cycle now?

So those are a couple of topics to be discussed in posts here in the future.

And, of course, politics, including geopolitics will probably intervene at various points.

Initially, I started this blog to explore issues I encountered in real-time business forecasting.

But I have wide-ranging interests – being more of a fox than a hedgehog in terms of Nate Silver’s intellectual classification.

I’m a hybrid in terms of my skill set. I’m seriously interested in mathematics and things mathematical. I maybe have a knack for picking through long mathematical arguments to grab the key points. I had a moment of apparent prodigy late in my undergrad college career, when I took graduate math courses and got straight A’s and even A+ scores on final exams and the like.

Mathematics is time consuming, and I’ve broadened my interests into economics and global developments, working around 2002-2005 partly in China.

As a trivia note,  my parents were immigrants to the US from Great Britain , where their families were in some respects connected to the British Empire that more or less vanished after World War II and, in my father’s case, to the Bank of England. But I grew up in what is known as “the West” (Colorado, not California, interestingly), where I became a sort of British cowboy and subsequently, hopefully, have continued to mature in terms of attitudes and understanding.

One Month Forecast of SPY ETF Price Level – Extreme Value Prediction Algorithm (EVPA)

Here is a chart showing backtests and a prediction for the midpoints of the monthly trading ranges of the SPY exchange traded fund.


The orange line traces out the sequence of actual monthly midpoints of the price range – the average of the high and low price for the month.

The blue line charts the backtests going back to 2013 and a forecast for September 2015 – which is the right-most endpoint of the blue line. The predicted September midpoint is $190.43.

The predictions come from the EVPA, an algorithm backtested to 1994 for the SPY. Since 1994, the forecast accuracy, measured by the MAPE or mean absolute percent error, is 2.4 percent. This significantly improves on a No Change model, one of the alternative forecast benchmarks for this series, and the OOS R2 of the forecast of the midpoint of the monthly trading range is a solid 0.33.

Just from eyeballing the graph above, it seems like there are systematic errors to the downside in the forecasts.

However, the reverse appears to happen, when the SPY prices are falling over a longer period of time.


I would suggest, therefore, that the prediction of about $190 for September is probably going to be higher than the actual number.

Now – disclaimer. This discussion is provided for scientific and entertainment purposes only. We assume no responsibility for any trading actions taken, based on this information. The stock market, particularly now, is volatile. There are lots of balls in the air – China, potential Fed actions on interest rates, more companies missing profit expectations, and so forth – so literally anything may happen.

The EVPA is purely probabilistic. It is right more often than wrong. Its metrics are better than those of alternative forecast models in the cases I have studied. But, withal, it still is a gamble to act on its predictions.

But the performance of the EVPA is remarkable, and I believe further improvements are within reach.

Multivariate GARCH and Portfolio Risk Management

Why get involved with the complexity of multivariate GARCH models?

Well, because you may want to exploit systematic and persisting changes in the correlations of stocks and bonds, and other major classes of financial assets. If you know how these correlations change over, say, a forecast horizon of one month, you can do a better job of balancing risk in portfolios.

This a lively area of applied forecasting, as I discovered recently from Henry Bee of Cassia Research – based in Vancouver, British Columbia (and affiliated with CONCERT Capital Management of San Jose, California). Cassia Research provides Institutional Quant Technology for Investment Advisors.


Basic Idea The key idea is that the volatility of stock prices cluster in time, and most definitely is not a random walk. Just to underline this – volatility is classically measured as the square of daily stock returns. It’s absolutely straight-forward to make a calculation and show that volatility clusters, as for example with this more than year series for the SPY exchange traded fund.


Then, if you consider a range of assets, calculating not only their daily volatilities, in terms of their own prices, but how these prices covary – you will find similar clustering of covariances.

Multivariate GARCH models provide an integrated solution for fitting and predicting these variances and covariances. For a key survey article, check out – Multivariate GARCH Models A Survey.

Some quotes from the company site provide details: We use a high-frequency multivariate GARCH model to control for volatility clustering and spillover effects, reducing drawdowns by 50% vs. historical variance. …We are able to tailor our systems to target client risk preferences and stay within their tolerance levels in any market condition…. [Dynamic Rebalancing can]..adapt quickly to market shifts and reduce drawdowns by dynamically changing rebalance frequency based on market behavior.

The COO of Cassia Research also is a younger guy – Jesse Chen. As I understand it, Jesse handles a lot of the hands-on programming for computations and is the COO.


I asked Bee what he saw as the direction of stock market and investment volatility currently, and got a surprising answer. He pointed me to the following exhibit on the company site.

Bee1 The point is that for most assets considered in one of the main portfolios targeted by Cassia Research, volatilities have been dropping – as indicated by the negative signs in the chart. These are volatilities projected ahead by one month, developed by the proprietary multivariate GARCH modeling of this company – an approach which exploits intraday data for additional accuracy.

There is a wonderful 2013 article by Kirilenko and Lo called Moore’s Law versus Murphy’s Law: Algorithmic Trading and Its Discontents. Look on Google Scholar for this title and you will find a downloadable PDF file from MIT.

The Quant revolution in financial analysis is here to stay, and, if you pay attention, provides many examples of successful application of forecasting algorithms.

Monday Morning Stock Forecasts May 18 – Highs and Lows for SPY, QQQ, GE, and MSFT

Look at it this way. There are lots of business and finance blogs, but how many provide real-time forecasts, along with updates on how prior predictions performed?

Here on BusinessForecastBlog – we roll out forecasts of the highs and lows of a growing list of securities for the coming week on Monday morning, along with an update on past performance.

It’s a good discipline, if you think you have discovered a pattern which captures some part of the variation in future values of a variable. Do the backtesting, but also predict in real-time. It’s very unforgiving.

Here is today’s forecast, along with a recap for last week (click to enlarge).TableMay18

There is an inevitable tendency to narrate these in “Nightly Business Report” fashion.

So the highs are going higher this week, and so are the lows, except perhaps for a slight drop in Microsoft’s low – almost within the margin of statistical noise. Not only that, but predicted increases in the high for QQQ are fairly substantial.

Last week’s forecasts were solid, in terms of forecast error, except Microsoft’s high came in above what was forecast. Still, -2.6 percent error is within the range of variation in the backtests for this security. Recall, too, that in the previous week, the forecast error for the high of MSFT was only .04 percent, almost spot on.

Since the market moved sideways for many securities, No Change forecasts were a strong competitor to the NPV (new proximity variable) forecasts. In fact, there was an 50:50 split. In half the four cases, the NPV forecasts performed better; in the other half, No Change forecasts had lower errors.

Direction of change predictions also came in about 50:50. They were correct for QQQ and SPY, and wrong for the two stocks.

Where is the Market Going?

This tool – forecasts based on the NPV algorithms – provides longer terms looks into the future, probably effectively up to one month ahead.

So in two weeks, I’m going to add that forecast to the mix. I think it may be important, incidentally, to conform to the standard practice of taking stock at the beginning of the month, rather than, say, simply going out four weeks from today.

To preview the power of this monthly NPV model, here are the backtests for the crisis months before and during the 2008 financial crisis.


This is a remarkable performance, really. Once the crash really gets underway in late Summer-Fall 2008, the NPV forecast drops in a straight-line descent, as do the actual monthly highs. There are some turning points in common, too, between the two series. And generally, even at the start of the process, the monthly NPV model provides good guidance as to the direction and magnitude of changes.

Over the next two weeks, I’m collecting high frequency data to see whether I can improve these forecasts with supplemental information – such as interest rates spreads and other variables available on a weekly or monthly basis.

In closing, let me plug Barry Eichengreen’s article in Syndicate An Economics to Fit the Facts.

Eichengreen writes,

While older members of the economics establishment continue to debate the merits of competing analytical frameworks, younger economists are bringing to bear important new evidence about how the economy operates.

It’s all about dealing with the wealth of data that is being collected everywhere now, and much less about theoretical disputes involving formal models.

Finally, it’s always necessary to insert a disclaimer, whenever one provides real-time, actionable forecasts. This stuff is for informational and scientific purposes only. It is not intended to provide recommendations for specific stock trading, and what you do on that score is strictly your own business and responsibility.

Mountain climbing pic from Blink.

Five Day Forecasts of High and Low for QQQ, SPY, GE, and MSFT – Week of May 11-15

Here are high and low forecasts for two heavily traded exchange traded funds (ETF’s) and two popular stocks. Like the ones in preceding weeks, these are for the next five trading days, in this case Monday through Friday May 11-15.


The up and down arrows indicate the direction of change from last week – for the high prices only, since the predictions of lows are a new feature this week.

Generally, these prices are essentially “moving sideways” or with relatively small changes, except in the case of SPY.

For the record, here is the performance of previous forecasts.


Strong disclaimer: These forecasts are provided for information and scientific purposes only. This blog accepts no responsibility for what might happen, if you base investment or trading decisions on these forecasts. What you do with these predictions is strictly your own business.

Incidentally, let me plug the recent book by Andrew W. Lo and A. Craig McKinlay – A Non-Random Walk Down Wall Street from Princeton University Press and available as a e-book.

I’ve been reading an earlier book which Andrew Lo co-authored The Econometrics of Financial Markets.

What I especially like in these works is the insistence that statistically significant autocorrelations exist in stock prices and stock returns. They also present multiple instances in which stock prices fail tests for being random walks, and establish a degree of predictability for these time series.

Again, almost all the focus of work in the econometrics of financial markets is on closing prices and stock returns, rather than predictions of the high and low prices for periods.

How Did This Week’s Forecasts of QQQ, SPY, GE, and MSFT High Prices Do?

The following Table provides an update for this week’s forecasts of weekly highs for the securities currently being followed – QQQ, SPY, GE, and MSFT. Price forecasts and actual numbers are in US dollars.


This batch of forecasts performed extremely well in terms of absolute size of forecast errors, and, in addition, beating a “no change” forecast in three out of four predictions (exception being SPY) and correctly calling the change in direction of the high for QQQ.

It would be nice to be able to forecast the high prices for five-day-forward periods with the accuracy seen in the Microsoft (MSFT) forecast.

As all you market mavens know, US stock markets experienced a lot of declines in prices this week, so the highs for the week occurred Monday.

I’ve had several questions about the future direction of the market. Are declines going to be in the picture for the coming week, and even longer, for example?

I’ve been studying the capabilities of these algorithms to predict turning points in indexes and prices of individual securities. The answer is going to be probabilistic, and so is complicated. Sometimes the algorithm seems to provide pretty unambiguous signals as to turning points. In other instances, the tea leaves are harder to read, but, arguably, a signal does exist for most major turning points with the indexes I have focused on – SPY, QQQ, and the S&P 500.

So, the next question is – has the market hit a high for a week or a few weeks, or even perhaps a major turnaround?

Deploying these algorithms, coded in Visual Basic and C#, to attack this question is a little like moving a siege engine to the castle wall. A major undertaking.

I want to get there, but don’t want to be a “Chicken Little” saying “the sky is falling,” “the sky is falling.”

Stock Market Predictability

This little Monday morning exercise, which will be continued for the next several weeks, is providing evidence for the predictability of aspects of stock prices on a short term basis.

Once the basic facts are out there for everyone to see, a lot of questions arise. So what about new information? Surely yesterday’s open, high, low, and closing prices, along with similar information for previous days, do not encode an event like 9/11, or the revelation of massive accounting fraud with a stock issuing concern.

But apart from such surprises, I’m leaning to the notion that a lot more information about the general economy, company prospects and performance, and so forth are subtly embedded in the flow of price data.

I talked recently with an analyst who is applying methods from Kelly and Pruitt’s Market Expectations in the Cross Section of Present Values for wealth management clients. I hope to soon provide an “in-depth” on this type of applied stock market forecasting model, which focuses, incidentally, on stock market returns and dividends.

There is also some compelling research on the performance of momentum trading strategies which seems to indicate a higher level of predictability in stock prices than is commonly thought to exist.

Incidentally, in posting this slightly before the bell today, Friday, I am engaging in intra-day forecasting – betting that prices for these securities will stay below their earlier highs.

Forecasts of High Prices for Week May 4-8 – QQQ, SPY, GE, and MSFT

Here are forecasts of high prices for key securities for this week, May 4-8, along with updates to check the accuracy of previous forecasts. So far, there is a new security each week. This week it is Microsoft (MSFT). Click on the Table to enlarge.


These forecasts from the new proximity variable (NPV) algorithms compete with the “no change” forecast – supposedly the optimal predictions for a random walk.

The NPV forecasts in the Table are more accurate than no change forecasts at 3:2 odds. That is, if you take into account the highs of the previous weeks for each security – actual high numbers not shown in the Table – the NPV forecasts are more accurate 4 out of 6 times.

This performance corresponds roughly with the improvements of the NPV approach over the no change forecasts in backtests back to 2003.

The advantages of the NPV approach extend beyond raw accuracy, measured here in simple percent terms, since the “no change” forecast is uninformative about the direction of change. The NPV forecasts, on the other hand, generally get the direction of change right. In the Table above, again considering data from weeks preceding those shown, the direction of change of the high forecasts is spot on every time. Backtests suggest the NPV algorithm will correctly predict the direction of change of the high price about 75 percent of the time for this five day interval.

It will be interesting to watch QQQ in this batch of forecasts. This ETF is forecast to decline week-over-week in terms of the high price.

Next week I plan to expand the forecast table to include forecasts of the low prices.

There is a lot of information here. Much of the finance literature focuses on the rates of returns based on closing prices, or adjusted closing prices. Perhaps analysts figure that attempting to predict “extreme values” is not a promising idea. Nothing could be further from the truth.

This week I plan a post showing how to identify turning points in the movement of major indices with the NPV algorithms. The concept is simple. I forecast the high and low over coming periods, like a day, five days, ten trading days and so forth. For these “nested forecast periods” the high for the week ahead must be greater than or equal to the high for tomorrow or shorter periods. This means when the price of the SPY or QQQ heads south, the predictions of the high of these ETF’s sort of freeze at a constant value. The predictions for the low, however, plummet.

Really pretty straight-forward.

I’ve appreciated and benefitted from your questions, comments, and suggestions. Keep them coming.