# Analysis of Time Series

• ### Mathematical Curve Fitting

Mathematical curve fitting is probably the most objective method of isolating trend. This method enables us to obtain precise estimates of the trend values based on some objective criterion. One of the major problems in using this method is the selection of an appropriate type of curve which best fit to the given data. However, […]

• ### Isolation of Cyclical Movements

The long term cyclical movements in a time series can be studied more or less in the same way as the seasonal movements. The data for the study of cyclical movements consists of large number of yearly observations and seasonal variations are assumed to be absent. The multiplicative model, as indicated earlier, is used to […]

• ### Seasonal Component Additive Model

Using the additive model i.e. , the de-trended series may be obtained by subtracting the trend values from the actual observations i.e., The remainder now consists of the seasonal and the residual components. The trend values that are subtracted might have been obtained by any of the methods described earlier, however, the moving trend or […]

• ### Seasonal Component Multiplicative Model

Using the multiplicative model i.e., the ratio detrended series may be obtained by dividing the actual observations by the corresponding trend values i.e., The remainder now consists of the seasonal and the residual components. The seasonal component may be isolated from the ratio-detrended series by averaging the detrended ratios for each month or quarter. The […]

• ### Merits and Demerits of Moving Average Method

Merits: Moving averages can be used for measuring the trend of any series. The method is applicable for linear as well as non-linear trends. Demerits: The trend obtained by moving averages is, in general, neither a straight line nor some standard curve. For this reason the trend cannot be extended for forecasting the future values. […]

• ### Method of Moving Averages

Suppose that there are times periods denoted by and the corresponding values of variable are . First of all we have to decide the period of the moving averages.  For short time series, we use period of 3 or 4 values. For long time series, the period may be 7, 10 or more. For quarterly […]

• ### Merits and Demerits of Semi-Averages Method

Merits: This method is very simple and easy to understandable and also it does not require much of calculations. Demerits: The method is used only when the trend in linear or almost linear. For non-linear trend this method is not applicable. It is used on the calculation of average and the average is affected by […]

• ### Method of Semi-Averages

This method is also simple and relatively objective than the free hand method. The data is divided in two equal halves and the arithmetic mean of the two sets of values of is plotted against the center of the relative time span. If the numbers of observations are even the division into halves will be […]

• ### Merits and Demerits of Free-Hand Curve

Merits: This method is very simple and easy to understand. It is applicable for linear and non-linear trends. It gives us a idea about the rise and fall of the time series. For every long time series, the graph of the original data enables us to decide about the application of more mathematical models for […]

• ### Method of Free-Hand Curve

It is familiar concept, briefly described for drawing frequency curves. In case of a time series a scatter diagram of the given observations is plotted against time on the horizontal axis and a freehand smooth curve is drawn through the plotted points. The curve is so drawn that most of the points concentrate around the […]

• ### Analysing the Secular Trend

A number of different methods are available to estimate the trend; however, suitability of these methods largely depends on the nature of the data and the purpose of the analysis. To measure a trend which can be represented as a straight line or some type of smooth curve, the following are the commonly employed methods. […]

• ### Analysis of Time Series

The object of the time series analysis is to identify the magnitude and direction of trend, to estimate the effect of seasonal and cyclical variations and to estimate the size of the residual component. This implies the decomposition of a time series into its several components. Two lines of approach are usually adopted in analyzing […]