Question

The following table contains information of 11 years of quaterly sales for KYRYH product

Year	Q1	Q2	Q3	Q4	Total
2006	37000	31000	27500	33800	129300
2007	38500	31700	27000	35000	132200
2008	40000	33000	28400	36000	137400
2009	41320	33000	29300	35800	139420
2010	42600	35200	30300	38400	146500
2011	42000	33000	28500	39000	142500
2012	43000	37800	32300	40600	153700
2013	47000	37000	31200	40000	155200
2014	46000	39000	28000	40500	153500
2015	49000	42300	33500	44000	168800
2016	52700	44000	33600	45700	176000

a) Determine the demand using mobile average

b) Comment on the validity of the model based on the confidence level of 95%

Answer 1

ARIMA

Call:
arima(x = t1$State, order = c(0, 0, 1))

Coefficients:
ma1 intercept
1.0000 532317.887
s.e. 0.0862 8065.284

sigma^2 estimated as 796544702: log likelihood = -561.95, aic = 1129.91

Training set error measures:
ME RMSE MAE MPE MAPE MASE ACF1
Training set 434.6242 28223.12 24476.33 -0.4190657 4.569171 4.436563 0.8137388

Exponential smoothing

Forecast method: Simple exponential smoothing

Model Information:
Simple exponential smoothing

Call:
ses(y = t1$State, h = 4, alpha = 0.2)

Smoothing parameters:
alpha = 0.2

Initial states:
l = 473812.6462

sigma: 20094.36

AIC AICc BIC
1138.961 1139.228 1142.704

Error measures:
ME RMSE MAE MPE MAPE MASE ACF1
Training set 14706.09 19671.27 17171.55 2.601553 3.122986 3.112504 0.8402502

Linear Regression

Call:

tslm(formula = State ~ trend, data = ts1)

Residuals:

Min 1Q Median 3Q Max

-34310 -7266 5109 13597 20552

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 442000.0 4761.4 92.83 <2e-16 ***

trend 3659.0 169.2 21.63 <2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16240 on 46 degrees of freedom

Multiple R-squared: 0.9105, Adjusted R-squared: 0.9085

F-statistic: 467.8 on 1 and 46 DF, p-value: < 2.2e-16

MAPE:  0.02580109

MSE: 252657325

Linear trend has the least MAPE so I would use that. Also, from the graph it is clear that linear trend gives the best result. The values of MAPE and MSE are all mentioned in the model results above.