Trend Projections
TREND PROJECTIONS: Seasonal Variations with Trends * is essentially concerned with the study of movement of variable through time. * requires a long and reliable time series data. * is used under the assumption that the factors responsible for the past trends in variables to be projected will continue to play their part in future in the same manner and to the same extend as they did in the past in determining the magnitude and direction of the variable.
Limitations:
* The first limitations of this method arise out of the assumption that the past rate of change in the dependent variable will persist in the future too. The forecast based on this method may be considered to be reliable only for the period during which this assumption holds. * Cannot be used for short-term estimates. * Cannot be used where trend is cyclical with sharp turning points of trough and perks. * If a time series exhibits a linear trend, the method of least squares may be used to determine a trend line (projection) for future forecasts. * Least squares, also used in regression analysis, determines the unique trend line forecast which minimizes the mean square error between the trend line forecasts and the actual observed values for the time series. * The independent variable is the time(t) period and the dependent variable is the actual observed value in the time series.
Trend Projection * Using the method of least squares, the formula for the trend projection is: Yt = b0 + b1t. where: Yt = trend forecast for time period t b1 = slope of the trend line b0 = trend line projection for time 0 t = time period Formulas in computing b1 and b0 : b1 = nS tYt - St SYt nSt 2 - (St )2 where: Yt = observed value of the time series at time period t =
Limitations:
* The first limitations of this method arise out of the assumption that the past rate of change in the dependent variable will persist in the future too. The forecast based on this method may be considered to be reliable only for the period during which this assumption holds. * Cannot be used for short-term estimates. * Cannot be used where trend is cyclical with sharp turning points of trough and perks. * If a time series exhibits a linear trend, the method of least squares may be used to determine a trend line (projection) for future forecasts. * Least squares, also used in regression analysis, determines the unique trend line forecast which minimizes the mean square error between the trend line forecasts and the actual observed values for the time series. * The independent variable is the time(t) period and the dependent variable is the actual observed value in the time series.
Trend Projection * Using the method of least squares, the formula for the trend projection is: Yt = b0 + b1t. where: Yt = trend forecast for time period t b1 = slope of the trend line b0 = trend line projection for time 0 t = time period Formulas in computing b1 and b0 : b1 = nS tYt - St SYt nSt 2 - (St )2 where: Yt = observed value of the time series at time period t =