Exploring Data Pattterns and Choosing a Forecasting Technique

Data patterns, including components such as trend and seasonality, can be studied using auto correlations. Auto correlation coefficient for different time lags of a variable are used to identify time series data patterns.

The formula for auto correlation is as follows:

If (Y t) is the actual time series value and k is the lag period and Y is the mean of the time series data values, then the auto correlation (r k) can be expressed as follows:

(r k) = sum of (Y t – Y) ( Y t-k – Y) from t = k+1 to t=n)/ sum of (Y t – Y)2 from t=1 to t= n

Example

A manufacturer of VCR sold last year for every month as follows:

January 123

February 130

March 125

April 138

May 145

June 142

July 141

August 146

September 147

October 157

November 150

December 160

Calculate the lag 1 auto correlation and state whether a regression analysis as an appropriate method to be used as a forecasting technique or to use more advanced forecasting technique such as for trend patterns, cyclical patterns, stationery patterns and seasonal patterns of Box-Jenkins forecasting method?

Solution

Using the auto correlation coefficient formula as mentioned above

r1 = 843/1474 = 0.572. This means that the successive monthly sales are somewhat correlated with each other. In this sense, regression analysis is not appropriate because for regression analysis the successive data must not have correlation to this extent to be used. There fore from the above lag I auto correlation a forecaster may have an insight to use a more advanced forecasting technique such as Box-Jenkins methods or any other method depending on the data patterns further analyzed for seasonal, cyclical components of the data and the randomness of the data patterns.

With the aid of auto correlation function a forecaster can study the auto correlations at different lag times and can answer the following issues or questions:

1. Are the time series data random?

2. Do the data have a trend? (non-stationery)

3. Are the data stationery?

4. Are the data seasonal?

If a series is random, the auto correlations between actual time series values and lagged values for a lag time are close to zero. The successive values of a time series are not related to each other.

If a series has a trend, successive observations are highly correlated and the auto correlation coefficients are typically significantly different from the first several time lags and gradually drop towards zero as the number of lags increases. The auto correlation for the time lag 1 is very large. (close to 1). The auto correlation for the time lag 2 will also be large. However, it wont be large compared to time lag1 auto correlation coefficient.

If a series has a seasonal pattern, a significant auto correlation will occur at the seasonal time lag or multiples of seasonal time lag. Seasonal time lag is 4 for quarterly data and 12 for monthly data.

Summary

As discussed above, a forecaster can choose an appropriate method of forecasting method by considering the purpose of forecasting, considering and analyzing the data using auto correlation analysis to determine the data patterns, accuracy and reliability as well as consistency of data itself,

Adequacy of the forecasting method for the purpose as well use of intuition and the ease with which it can be used by users and whether it may used by the users. If quantitative and qualitative methods are used appropriately given the organizational constraints and cost a forecasts become accurate as well as usable for effective decision making. The overriding factor in choosing the appropriate technique is not accuracy at the expense of usability. If forecasts are not used or not understood by decision makers even it is accurate then it becomes ineffective. Put it in other words sophisticated forecasting techniques always wont be an effective method in all circumstances. Careful consideration of the fators as discussed above is paramount in choosing a forecasting method.