STATISTICS

Time Series Data

by George R. Arrington, Ph.D.
While time series data is the heart of most technical trading systems, some have a tendency to reflect seasonal patterns; for example, agricultural commodities tend to follow harvest cycles. Here's how to adjust data to see nonseasonal patterns more clearly.

Time series data, which is data such as most price and volume data collected sequentially over time and usually at fixed intervals, is the basic fuel for most technical trading systems. As new data becomes available, it is used to recalculate the value of technical indicators. This, in turn, may trigger a trading signal. Time series data often contains a bias that reflects seasonal patterns; for example, prices of agricultural commodities tend to follow harvest cycles and seasonal patterns of consumption. Many other economic variables, such as employment, money supply, heating oil demand, and sales of new automobiles, also exhibit significant seasonal variation.

Often, it is easy to understand why these seasonal variations occur, but they make it difficult to analyze and understand the time series data. If the price of a wheat futures contract goes down by 10 cents during August, for instance, it would be helpful to know how much of that drop can be attributed to normal seasonal patterns and how much can be attributed to other factors.

If we use time series data as part of a technical trading system or to analyze trends, we may want to separate the normal seasonal variation to see nonseasonal patterns more clearly. This process is known as seasonal adjustment. Many widely published economic statistics, such as the unemployment rate and the consumer price index (CPI), are seasonally adjusted before being published.

RATIO TO MOVING AVERAGE METHOD

In general, it is difficult to calculate seasonal adjustment factors. The procedure used by the Bureau of Labor Statistics, for example, is very complicated. Here's a relatively simple method for doing seasonal adjustments, known as the ratio to moving average method.

In this example, let us start with the raw data (seasonally unadjusted) in Figure 1, which is the monthly volume of trading on the American Stock Exchange over the past five years.

FIGURE 1: ASE VOLUME-SEASONALLY UNADJUSTED. Here is the average daily volume (in thousands) of shares traded on the American Stock Exchange. These figures are seasonally unadjusted and are shown for each month for 1993 through June 1998.

George R. Arrington works for the Federal Reserve System in New York City.