Question

3. The following table shows the prevailing interest rates (in %) in HK over the last 10 years. Year 2005 2006 20072008200920102011201220132014 Rate 6.255.56.55 4.55.75 3.5311.25 The following summary statistics are provided for you: t 55Xrate-42.25 yxrate-183.75 Σ.385 Σrate-213.6875 where t-time period-1,2,.,10.Assuming t-1 for 2005, t 2 for 2006, etoc. (a) Using a smoothing coefficient of α = 0.90, exponentially smooth the series and forecast for 2015. (b) Using a smoothing coefficient of a0.30, exponentially smooth the series and forecast for 2015 (c) Explain the difference in your answers for parts (a) and (b). (d) Fit a linear trend line to the data and forecast for 2015. Compare the result with those of exponential smoothing.

Answer 1

a) we forecast the values using the formula

$F_{t+1}=\alpha*A_t+(1-\alpha)*F_{t}$

Given $\alpha=0.90$;$F_{t+1}=0.90*A_t+0.10*F_{t}$

Given $\alpha=0.30$;$F_{t+1}=0.30*A_t+0.70*F_{t}$

0.81461802 Standard Em 0.90290986 Slope 0.58939394 Intercept 7.46666667

90 0.30 ar 87 2005 2006 2007 2008 2009 201 201 201 2013 2014 2015 25 25 5.575 6.4075 .5 5.14075 6.289 25 6.025 5.8525 6.5 5.7 98525 3.933 4.522 3.344 , 2.166 75 4.564075 4.948525 3.5 5.6314075 4.9198525 3 3.71314075 4.99198525 1 3.07131408 3.49919853 1.20713141 2.44991985 1.24571314 1.21999199 1.5 0.9

A linear trend line is fitted with EXCEL and the results are in the column d)

The forecast for the year 2015 for method in a),b) and d) are respectively 1.246,1.22 and 0.988

c)The older observations are given more weights than current year for which forecast is made as the value of $\alpha$ increases. But when the value of $\alpha$ is 0.30 more weights are given to previous year forecast than observations. So in the column b you can see Forecast values are closer to the previous year forecasts where as in the column a) forecast values are more closer with the previous year actual values.

Forecasting values using linear trend equation has most of the values having less difference with the actual values. So Its forecast on 2015 can be relied more than that done using exponential smoothing.