In an analogous manner we shall proceed in case of twelve month seasonality.Īnother regression method for eliminating seasonal component is based on the fact that this component is estimated by means of a suitably selected mathematical function. Is the “average” of seasonal regression parameters. In case of the regression model with artificial variables we shall adjust the estimated trend and the seasonal factors, , to the form of : Forecasting requires us to choose the time variables in the horizon of h > 0 and for the seasonal variables, substitute the unit values of the respective seasons in the horizon h. The estimated regression model (3) can be used for the construction of point and interval forecasts. Particularly important is to test the heteroscedasticity and autocorrelation of the random component. The verification of the suitability of the regression model (1) is analogous to that in any other regression model. The estimated model will take the form of: Model parameters can be estimated using the least square method. Model (1) contains a trend, seasonal and random component. The artificial variable is a zero vector and the effect of the first quarter is included in the intercept β 0 of the linear trend, which is interpreted in terms of the base level of the studied variables. Since the artificial variable attains the value of one in a particular observation, we declare that in this period, to the value generated from a linear trend we shall add the value of seasonal fluctuations, which is calculated compared to the base period, which is in this case the first quarter of the year. Of length of which is equal to n number of the time series of observations. Where the artificial variables are defined as vectors Furthermore, we assume that the time series has a linear trend and quarterly seasonality. In the presence of free parameter (constant) in the model trend, in order to avoid multicollinearity, seasonality is modeled as a qualitative variable using the s – 1 of artificial variables, where s is the length of the season included in the time series. Let us assume an additive time series model in which the value of the indicator y t in the tperiod is given by the sum where T t is the trend component, S t is the seasonal component and ε t is a random component. The seasonal component is expressed using artificial (zero unit) variables that assign a value to the time series unit in case it is found in the considered season and zero otherwise. The trend component is modeled via suitable regression function, for example line, parabola, and so on. Artificial variable is used to quantify the effect of the respective period on the estimated value of the investigated variables. In the construction of the forecasts of seasonal time series, a regression model with artificial (dummy) variables with simultaneously estimated trend and seasonality parameters can be used. Regression Approaches to the Seasonal Component of Time Series the Winters exponential smoothing is applied. In case, where the nature of the seasonal component may change, e.g. To eliminate seasonal component regression methods based on the theory of linear regression model are also used. Often they apply different types of moving averages, which eliminate from the time series the components the frequency of which does not exceed the number of observations forming the moving average length. There are many methods of seasonal adjustment and their classification is not easy, because in practice the techniques used are a combination of several methods. The aim of seasonal adjustment is to uncover the underlying dynamics in the development of the investigated phenomena and allow a direct comparison of their development in different seasons within the year. When working with time series, the data must be adjusted seasonally. If we analyze the evolution of time series, we are interested not only in the main development trend of the indicators, but also in the course and intensity of any periodic fluctuations, which these time series present.
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