## 阿德萊德代寫assignment

**2.1.Description of data**

Before do the forecasting for the data, it is necessary to explore the form of it. The trend of wine is showed in figure 1 and the trend of brandy in figure 2. We can see that both of them contain a seasonal factor, which make the sales data changes in four seasons within a years while the changes of trend of same seasons keeps steady. Trends in the whole of the data are opposite between wine and brandy. The sales of wine go higher along the time and the sales of brandy goer down despite the seasonal effects. The it is obviously that the sales of the wine keeps steady in the part of the previously time, which means it did not change much in the earlier time. It may be the policy factors that affect the industry. It can be inferred that since that time, the government put forward some policies or support some relevant institutions to make the industry recover and begin to develop.

**2.2.Forecasting**

There are many kinds of forecasting method for time series data. The conclusion can be drawn from the descriptive of data that these two data sets both change as time goes with the factor of seasons. In this situation, such method may be suitable. Sincea method that produces accurate forecasts in one case may not be appropriate and produce accurate forecasts in another case. So it is necessary to try many methods and then pick out the most suitable one. So the methods for these data sets can be the Winters Exponential Smoothing, Decomposition, Autoregressive models and seasonal ARIMA.

**2.2.1.Winters Exponential Smoothing:**

Timeseriesmayexhibitaseasonalcomponent (pattern) due to influences of weather, holiday periods, weekends etc. The Holt-Winters (HW) method is often used to produce short-term forecasts when the data contain a trend and a seasonal pattern. Based on the fact that the time series data exhibit significant seasonal components, we employ the Winters Exponential Smoothing model to fit the original data.

The predicted value of past periods and the residuals are compute and stored and model with the Multiplicative type of Seasonality performs well than with Additive type. Judge from the MAPE (Mean Absolute Percent Error), the model fits well with wine 6 and brandy 12.42. Other important results are showed in the Table1.

Table1

Wine | Brandy | ||||

MAPE | MAD | MSE | MAPE | MAD | MSE |

6 | 4911 | 46911807 | 12.42 | 32.2 | 2110.2 |

However, by examining the residuals carefully, we will find it not so well as shown in the Table 2. The autocorrelation coefficients for these residuals are shown in Table 2and Figure 2. Significant autocorrelation coefficients indicate some association or pattern in the residual and the LBQ statistic also rejects the hypothesis that the residuals are drawn from a random series. So, we can judge the model to be inadequate in fitting the data.