A time series is a sequence of observations which are ordered in time (or space). If observations are made on some phenomenon throughout time, it is most sensible to display the data in the order in which they arose, particularly since successive observations will probably be dependent. Time series are best displayed in a scatter plot. The series value X is plotted on the vertical axis and time t on the horizontal axis. Time is called the independent variable (in this case however, something over which you have little control). There are two kinds of time series data: - Continuous, where we have an observation at every instant of time, e.g. lie detectors, electrocardiograms. We denote this using observation X at time t, X(t).
- Discrete, where we have an observation at (usually regularly) spaced intervals. We denote this as Xt.
Examples
Economics - weekly share prices, monthly profits
Meteorology - daily rainfall, wind speed, temperature
Sociology - crime figures (number of arrests, etc), employment figures
 We want to increase our understanding of a time series by picking out its main features. One of these main features is the trend component. Descriptive techniques may be extended to forecast (predict) future values. Trend is a long term movement in a time series. It is the underlying direction (an upward or downward tendency) and rate of change in a time series, when allowance has been made for the other components. A simple way of detecting trend in seasonal data is to take averages over a certain period. If these averages change with time we can say that there is evidence of a trend in the series. There are also more formal tests to enable detection of trend in time series. It can be helpful to model trend using straight lines, polynomials etc. Cyclical Component We want to increase our understanding of a time series by picking out its main features. One of these main features is the cyclical component. Descriptive techniques may be extended to forecast (predict) future values. In weekly or monthly data, the cyclical component describes any regular fluctuations. It is a non-seasonal component which varies in a recognisable cycle.
Seasonal Component We want to increase our understanding of a time series by picking out its main features. One of these main features is the seasonal component. Descriptive techniques may be extended to forecast (predict) future values. In weekly or monthly data, the seasonal component, often referred to as seasonality, is the component of variation in a time series which is dependent on the time of year. It describes any regular fluctuations with a period of less than one year. For example, the costs of various types of fruits and vegetables, unemployment figures and average daily rainfall, all show marked seasonal variation. We are interested in comparing the seasonal effects within the years, from year to year; removing seasonal effects so that the time series is easier to cope with; and, also interested in adjusting a series for seasonal effects using various models.,, Irregular Component We want to increase our understanding of a time series by picking out its main features. One of these main features is the irregular component (or 'noise'). Descriptive techniques may be extended to forecast (predict) future values. The irregular component is that left over when the other components of the series (trend, seasonal and cyclical) have been accounted for. Download 1 Download 2 
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