Content1. Trend forecasting2. Forecast estimation

TOPIC IV. TREND FORECASTING

Trend forecasting is technique of time series forecasting which uses statistical methods in order to predict future patterns of time series data.

Trend forecasting is used to predict future data by relying on historical (past) data.

Trend forecasting

Trend forecasting may be used to determine a trend line (projection) for future forecasts. The linear trend is any long-term increase or decrease in a time series in which the rate of change is relatively constant.

Trend is often shown graphically (as line graphs) with the level of a dependent variable on the y-axis and the time

period on the x-axis

For example, having statistics on company profit for 5 years (table 1) you can find the profit forecast for the next period t = n +1=5+1=6

(for 2014, because 2014 is the sixth period).

• 1-st step: Select the equation.

• 2-d step: Calculate the forecast based on trend equation.

• 3-d step: Estimate the forecast.

Three steps in trend forecasting

Trend equation is used to determine the trend in the variable y, which can be used to forecasting.

Linear equation describes the process when the economic data increase or decrease by more or less constant value. Linear equation looks like:

where a and b – are the linear coefficients;

t – is the independent variable (time – years, quarters, months).

1-st step: Select the equation

tbаy t ^

Linear coefficients

For example: statistical data on demand for products for 10 months are given in the table 2. Calculate the demand forecast for January and

February using trend forecasting.

Calculation results

Calculation results

2-d step: Calculate the forecast based on trend equation

Demand forecast with trend forecasting

• Coefficient of determination

• Correlation coefficient

• Absolute forecast error

• Mean forecast error

• Mean squared forecast error

• Root mean squared forecast error

• Mean percentage error

3-d step: Estimate the forecast

• values between 0 and 0,3 indicate a weak positive linear relationship;

• values between 0,3 and 0,7 indicate a moderate positive linear relationship;

• values between 0,7 and 1 indicate a strong positive linear relationship.

Coefficient of determination (R2) – is a measure used in trend analysis to assess how well a linear equation

explains and predicts future outcomes

The following points are accepted guidelines for interpreting the correlation coefficient:• 1) 0 indicates no linear relationship;

• 2) +1 indicates a perfect positive linear relationship: as one variable increases in its values, the other variable also increases in its values;

• 3) -1 indicates a perfect negative linear relationship: as one variable increases in its values, the other variable decreases in its values;

• 4) values between 0 and 0,3 (0 and -0,3) indicate a weak positive (negative) linear relationship;

• 5) values between 0,3 and 0,7 (-0,3 and -0,7) indicate a moderate positive (negative) linear relationship;

• 6) values between 0,7 and 1 (-0,7 and -1) indicate a strong positive (negative) linear relationship.

Correlation coefficient is the square root of the coefficient of determination

Measurement of the forecast accuracy

Measurement of the forecast accuracy

For example: statistical data on demand for products for 10 months are given in the table 2. Calculate the absolute forecast error, mean

forecast error, mean squared forecast error, root mean squared forecast error, mean percentage error, correlation coefficient and

coefficient of determination.

Calculation results

Calculation results

Correlation coefficient (r) is a square root of the coefficient of determination

approximately 78% (0,78*100%) of the variation in the dependent variable (demand) can be explained by the linear equation.

78,0614,0 r