Time Series Analysis - Lecture Note 3

Measurement of Trend

In time series analysis Trend is a long-term movement. This component represents the basic tendency of the series. The following methods are generally used to determine trend in any given time series.

1) Method of moving average 

2)Method of least squares (Curve fitting)

Method of Moving Average

It is a method for computing trend values in a time series that eliminates the short-term and random fluctuations from the time series by means of moving average. Moving average of a period m is a series of successive arithmetic means of m terms at a time starting with 1st, 2nd, 3rd, and so on. The first average is the mean of first m terms; the second average is the mean of 2nd term to (m+1)th term and 3rd average is the mean of 3rd term to (m+2)th term and so on.

If m is odd then the moving average is placed against the mid-value of the time interval it covers. But if m is even then the moving average lies between the two middle periods which does not correspond to any time period. So further steps have to be taken to place the moving average to a particular period of time. For that, we take a 2-yearly moving average of the moving averages which correspond to a particular time period. The resultant moving averages are the trend values.

Advantages: 

I) This method is simple to understand and easy to execute. 

II) It has flexibility in application in the sense that if we add data for a few more time periods to the original data, the previous calculations are not affected and we get a few more trend values. 

III) It gives a correct picture of the long-term trend if the trend is linear.  If the period of moving average coincides with the period of oscillation (cycle), the periodic fluctuations are eliminated. 

IV) The moving average has the advantage that it follows the general movements of the data and that its shape is determined by the data rather than the statistician's choice of a mathematical function.

Disadvantages: 

I) For a moving average of 2m+1, one does not get trend values for the first m and last m periods.

II) As the trend path does not correspond to any mathematical function, it cannot be used for forecasting or predicting values for future periods.

III) If the trend is not linear, the trend values calculated through moving averages may not show the true tendency of data. 

IV) The choice of the period is sometimes left to the human judgment and hence may carry the effect of human bias.