# time-series analysis

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## Time-series analysis

Assessment of relationships between two or among more variables over periods of time.

## Time-Series Analysis

An analysis of the relationship between variables over a period of time. Time-series analysis is useful in assessing how an economic or other variable changes over time. For example, one may conduct a time-series analysis on a stock to help determine its volatility.
Fig. 184 Time-series analysis.

## time-series analysis

the analysis of past statistical data, recorded at successive time intervals, with a view to projecting this experience of the past to predict what will happen in the (uncertain) future. Thus, time-series information can be used for FORECASTING purposes.

Fig. 184 shows a typical time series. The fluctuations in time-series data, which inevitably show up when such series are plotted on a graph, can be classified into four basic types of variation that act simultaneously to influence the time series. These components of a time series are:

1. SECULAR TREND, which shows the relatively smooth, regular movement of the time series over the long term.
2. cyclical variation, which consists of medium-term, regular repeating patterns, generally associated with BUSINESS CYCLES. The recurring upswings and downswings in economic activity are superimposed upon the secular trend.
3. seasonal variation, which consists of short-term, regular repeating patterns, generally associated with different seasons of the year. These seasonal variations are superimposed upon the secular trend and cyclical variations.
4. irregular variations, which are erratic fluctuations in the time series caused by unpredictable, chance events. These irregular variations are superimposed upon the secular trend, cyclical variations and seasonal variations.

Time-series analysis is concerned with isolating the effect of each of these four influences upon a time series with a view to using them to project this past experience into the future. In order to identify the underlying secular trend in a time series, the statistician may use REGRESSION ANALYSIS, fitting a line to the time-series observations by the method of ordinary least squares. Here, time would serve as the INDEPENDENT VARIABLE in the estimated regression equation and the observed variable as the DEPENDENT VARIABLE. Alternatively, the statistician may use a moving average to smooth the time series and help identify the underlying trend. For example, he could use a five-period moving average, replacing each consecutive observation by the average (MEAN) of that observation and the two preceding and two succeeding observations.

Exponential smoothing provides yet another technique that can be used to smooth time-series data. It is similar to the moving-average method but gives greater weight to more recent observations in calculating the average. In order to identify the effect of seasonal variations, the statistician can construct a measure of seasonal variation (called the seasonal index) and use this to deseasonalize the time-series data and show how the time series would look if there were no seasonal fluctuations.

Once the trend has been identified, it is possible to EXTRAPOLATE that trend and estimate trend values for time periods beyond the present time period. In Fig. 184, for example, the trend for time periods up to and including time t can be extrapolated to time t + 1. Extrapolating thus becomes a method of making predictions or forecasts, although the accuracy of these forecasts will depend critically upon whether underlying forces that affected the time series in the past will continue to operate in the same way in the future.

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