A moving average system is used for forecasting weekly demand. $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ are sequences of forecasts with parameters $${m_1}$$ and $${m_2}$$, respectively, where $${m_1}$$ and $${m_2}\left( {{m_1} > {m_2}} \right)$$ denote the numbers of weeks over which the moving averages are taken. The actual demand shows a step increase from $${d_1}$$ to $${d_2}$$ at a certain time. Subsequently,

The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth year was $$876$$ units. If the forecast for the fifth year, using simple exponential smoothing, is equal to the forecast using a three period moving average, the value of the exponential smoothing constant $$\alpha $$ is

The sale of cycles in a shop in four consecutive months are given as $$70, 68, 82 95.$$ Exponentially smoothing average method with a smoothing factor of $$0.4$$ is used in forecasting. The expected number of sales in the next month is

In a time series forecasting model, the demand for five time periods was $$10, 13,$$ $$15,$$ $$18$$ and $$22.$$ A linear regression fit resulted in an equation $$F = 6.9 + 2.9$$ $$t$$ where $$F$$ is the forecast for period $$t$$. The sum of absolute deviations for the five data is