Forecasting III

Part II : https://tulsipatro29.medium.com/forecasting-ii-67658098ace7
Part I : https://tulsipatro29.medium.com/an-introduction-to-forecasting-5d293c6c9f5f

Exponential Smoothing

Exponential Smoothing is used to weight data from previous time periods with exponentially decreasing importance in the forecast. It is accomplished by multiplying the actual value for the present time period, by a value between 0 and 1 (the exponential smoothing constant) referred to as α and adding the result to the product of the present time period’s forecast and
(1-α).

The value of α is determined by the forecaster. The essence of this technique is that the new forecast is a combination of the present forecast and the present actual value.
If α is chosen to be less than 0.5, less weight is placed on the actual value than on the forecast of that value.
If α is chosen to be greater than 0.5. more weight is being put on the actual value than on the forecast value.

For example, the prime interest rate for a time period is 5% and the forecast of the prime interest rate for the time period was 6%; then the forecast of the prime interest rate for the next period is determined by exponential smoothing with α = 0.3, and the forecast value will be,

The smaller the α is, the less impact the error has on the new forecast and the more the new forecast is like the older one. It demonstrates the dampening effect of α on the forecasts.

Trend Analysis

Trend analysis can be done using Regression Analysis or it can be described as “Time-Series Regression Trend Analysis” where the response variable Y is the variable being forecast and the independent variable X represents time.

Linear Regression Trend Analysis :

Holt’s Two-Parameter Exponential Smoothing method

Exponential smoothing is appropriate to use in forecasting stationary time-series data but is ineffective in forecasting time-series data with a trend because the forecasts will lag behind the trend.
Holt’s technique uses weights β to smooth the trend in a manner similar to the smoothing used in single exponential smoothing α.
The model forecasts includes both a smoothing value and a trend value.

Seasonal Effects

Seasonal effects are patterns of data behaviour that occur in period of time of less than one year.

DECOMPOSITION
Decomposition is used to isolate the effects of Seasonality.
It uses the multiplicative model as its basis.
T.C.S.I
where T = trend,
C = cyclicality
S = seasonality
I = irregularity
According to this model, the data can contain the elements of trend, cyclical effects, seasonal effects and irregular fluctuations. The process of isolating the seasonal effects is determined by finding the T.C for each value and dividing the time series data (T.C.S.I) by T.C

The resulting expression contains seasonal effects along with irregular fluctuations which can also be removed, leaving only the seasonal effects.