(originally posted 02/05/07 on Wobbly Universe blog by Ray Tomes)

Although I had been somewhat interested in cycles before 1978, that was the year when I began doing economic modelling on a computer and some cycles just jumped out at me uninvited, and a long time serious interest in cycles began. I did work at that time for a number of Corporations, both large ones and small ones that were about to become large. I developed my own techniques for doing this, and eventually became convinced that this method is better than the methods used by many economists.

This study was performed at a time when the NZ economy was not an open one and some corporations wanted to predict possible future changes in the exchange rate, changes in interest rates and in inflation. Data were gathered for the last 44 years and included anything related to the New Zealand economy:- import and export prices and volumes by various major categories; stocks of major NZ production items; terms of trade; share prices; several price and inflation indices; a variety of demographic data; births, deaths and marriages; mortgages and land and building prices and transfers; wages. The analysis used the base variables and also the annual rate of change of them because that is often what is desired to be predicted.

All these variable were processed by a method known as factor analysis. What this does is to take many variables and reduce them to a much smaller number that still contains the essence of the original, in that the original data is very largely explained as each item being affected by several of these factors, with the balance taken as being to some extent noise. In this study, 9 independent (that is uncorrelated) factors were extracted and this report shows graphs of these. When considering any of the original variables or its rate of exchange, nearly all of the variables can be well explained as the sum of a combination of the factors with various loadings.

The factors are displayed below:

It can be seen that the first two factors are rather slow moving ones that show the general state of the economy and it is suggested that these are related to the Kondratieff cycle which is recognised as being about 53 years. Factors 3 and 4 show a moderately regular cycle with a period varying between 3 and 4 years. These two variables are related in the same way that a sine and cosine wave are (or an electric and magnetic field for that matter) with factor 4 being a reasonable measure of the rate of change of factor 3 and factor 3 being a reasonable measure of the negative rate of change of factor 4. These two together are what is generally called the business cycle.

Factor 6 shows a quite regular cycle of close to 3 years although it shows two periods of heightened amplitude around 1957-60 and 1972-74. These two periods correspond to brief periods (3 years each) when the country had Labour governments in between longer periods of National government. However the timing allows the conclusion that the cause of the cycle was not the change in government but perhaps the other way around.

The other factors are not so clearly defined as cycles, although there is some presence of cyclical activity. They are less well defined, but have specific meanings in terms of which variables they correlate with.

In order to try and predict future economic conditions, multiple regression equations were found that use the 9 factors to predict each of the factors in turn from the previous years values for those factors. This works particularly well for factors 3 and 4 because, as mentioned, each variable is closely related to the rate of change of the other.

Before trying to predict the future, it is always best to try and predict the past to see if the method is reasonably sound.

So here are two test runs of the method compared to what actually happened. One test was started in 1960 and the other in 1973. The choice of 1973 was made because the so-called oil shock happened in 1974 and lead to major disruption in world prices and economies, and is considered to have been a random rather than a predictable event.

However the test shows that the regression equations predict the big swing in factor 3, actually slightly over-estimating it. Factor 3 is negatively correlated with many economic variables and so goes up when the economy crashes – the things related to it are terms of trade and export prices and volumes. NZ is harder hit by this factor than most countries.

In most cases the predictions are moderately accurate for about 5 years ahead after which the forecasts become a bit sterile compared to the economic movements that actually happen.

The next step is to use the data to make real predictions about the future.

*It has been said that prediction is a difficult business, especially about the future.*

These forecasts were supplied to several corporations and also I gave a talk at the NZ Statistical Association Conference. It was well received, except that several economists had some criticisms. They told me that the long cycle that seemed to exist in factor 1 (and perhaps 2) was called the Kondratieff cycle and also named another cycle or two and then told me that these cycles did not exist. I was very puzzled as to why cycles that didn’t exist appeared in my data and why that had been given names! However participants other than economists said that some of the other cycles were exactly what they experienced in their own areas of study.

These predicted values for the factors are then used to work backwards to the original variables and give the clients what they wanted to know. My prediction of inflation continuing at a level of around 15% for at least 5 years was very markedly different from NZ Reserve Bank and other economists who were predicting a rapid decline towards 5% in 3 or 4 years time. My prediction was the one that was right.

In my report to my client, I was able to make quite an accurate prediction of the share market for the next few years and to state that there would be no more devaluations of the NZ$ as there had been several in the previous few years. There were no errors in my forecasts.

**Conclusion**

This method of reducing economic variables to a small number of factors that still contains the essence of the data is a valuable method that overcomes several serious problems in economic modelling. Firstly, there is usually insufficient historical data and models become over specified and mathematically are not sound. The use of factors also removes noise and the factors are much crisper and cleaner data.

There are other methods that are also better than traditional modelling methods, such as Box-Jenkins ARIMA models etc. These methods are mathematically based and assume no economic knowledge and they work. The economic understanding models are generally less accurate. I have not compared my method to Box-Jenkins, which uses only one variable to,predict any variable — itself! I suspect that this method would allow an improvement on Box-Jenkins, because in the case of factors like 3 and 4, they do show that there is momentum in the economy that moves from one variable to another.

*For 4 years from early 2007 until late 2010, Ray Tomes ran a blog called “Wobbly Universe” on his personal web site. With software changes that blog stopped working. Over the coming weeks or months these old articles will be reposted to CRI blog.*