# Time Series Analysis Paper

Time series is a collection of observations made sequentially in time. That is, it is an arrangement of statistical data in accordance with time. There are several examples of tome series. The economic time series which deal with share prices, average income in successful months or the average export totals in successful months. Also, there is the physical time series for example rainfall, humidity, temperature and others. There is also the demographic time series which are concerned with population such as population density and others. There is also the marketing time series which include marketing in successful months or days.

Time series have several objectives. There is the descriptive purpose. This is seen when plotting a specific data; the first step is to obtain the descriptive measures of the main properties of the series. Second, there is the explanation purpose. This occurs after observations are taken on two or more variables; it may be possible to use the prediction in one variable to explain variation in the other variable.

Next, is the prediction purpose.This is where in an observed time series, future values of the time series may be predicted. Also, there is the control purpose. This is where we use the structural model devised to control the system by either generating warning signs of future events or to know what would happen if the system is altered. Lastly, there is statistical model building. Here, several jointly independent variables are considered to come up with a statistical model.

#### Trend Analysis

Trend is the general tendency of the data to increase or decrease over a long period of time. An example is data concerning population over time where we can have an upward or downward tendency. An upward tendency is usually seen in data concerning population, currency in circulation whereas a downward tendency is seen in data concerning birth, death and epidemics.

Trend comes about due to the forces which are either constant or change gradually over a long period of time. It should also be noted that in this case, the term long period of time is relative since it is defined differently in different situations.

There are several ways of measuring time series containing trend. This depends on whether one wants to measure/estimate the trend or whether one wants to remove the trend in order to analyse local fluctuations. The measurement of trend can be carried out in several ways; graphical method, method of semi-averages, method of curve fittings and the method of moving averages.

#### Forecasting

This is estimating of future events of a time series. There are many forecasting procedures available. Some of them include; Box-jenkinsprocedure, exponentialsmoothing, extrapolation of trend curves, multiple regression and stepwise auto regression.

Forecasting methods are broadly classified to three groups. There is the subjective method. This is where forecasts are made on a subjective basis using judgement, intuition, commercial knowledge or any other measurement of knowledge. There is also the univariate method. This is where forecasts of a given variable are based on a model fitted only to past observations. Lastly, there is the multivariate method. Here, a forecast of a given variable depends on at least partly on values of one or more other series called the predictive or explanatory variables.