Electricity is the basic demand for peoples’ daily life, and relate to the Industrial production. It is also be a very important indexer to indicate the economic growth because the electricity demand and the economic growth always highly related. Thus the prediction of the electricity demand is very important. The government of a country must be able to forecasting the electricity demand in order to formulate its policies. This paper will conduct an analysis for the Chinese Electricity demand, and provide some useful model to predict the electricity demand in the future. 2. Time series data for Electricity demand of China
Monthly electricity generation of China from 1999 to 2004 is shown in table 1. Plot the data on Figure 1, it can be shown that the demand of electricity was growing during these six years. From the chart, the growth trend can be easily indentified. The pattern of the trend will be discussed in following section. The monthly electricity data present some seasonal changed pattern, the July and August seem like the peak of each year, more detail should be discussed in later section.
Table 1: Chinese Monthly Electricity Generation
Source: Chinese yearly statistical Data, www.stats.gov.cn
Figure 1: Electricity Generation plot versus time
3. Modelling trend by using Polynomial Functions
From the plot versus time, there is obviously trend during this period. This section regression this Electricity Generation by two trend model: linear trend model and Quadratic trend model. 4.1. Linear Trend Model
The trend model can be written as:Yt=TRt+εt
Yt= the value of Electricity Generation in period t
TRt= the trend in period t
εt= the error term in period t
Linear trend: TRt=β0+β1t
Regression result: yt=85.19+1.28t
The t-statistic for β1is 22.32 and P-value less than 0.0001, this indicates there is extremely strong evidence to reject the non-trend hypothesis. And the R square data is 0.877, which show this regression is a good estimate for the electricity generation. Analyze the residuals to check the regression. The result shows that the F-statistic is 498.12, which indicate that the regression is significant.
Figure 2: Linear Trend Regression Residual plot
4.2. Quadratic trend model
From above analysis, the linear trend model can be a good one to describe the trend of electricity generation during these six years. However, a further look at the residual plot, figure 2, will find that the residual not distributed randomly. The residuals for the first 20 month are almost positive, the following data show negative appearance. This appearance might be indicated that the trend is actually bending during this time. Thus add the square item to model a Quadratic trend Model for the electricity is needed to eliminate this error. Quadratic trend: Yt=β0+β1t+β2t2
The regression result: yt=98.717+0.182t+0.015t2
The t-statistic for the square item is 5.95 while the linear item only 0.95. Although the P-value is low for the linear portion, for there is extremely strong evidence to have square part, the linear portion also needed to be remained. To compare with the linear trend model, the quadratic model has a larger R-square value, say 0.919. This might indicate that the Quadratic Model can predict more accurate than the linear trend model.
Figure 3: Quadratic Trend Model Regression Residual Plot
4. Autocorrelation Detection
From previously discussion, we find the quadratic trend model can be fit the time series of the electricity generation of China from 1999 to 2004. One of the important assumptions of the Quadratic trend model is that the error item should be random and independent. If this independence assumption violated in this model, some cycle factor might be take in account for a more accurate prediction. This section will conduct a Durbin-Watson Test for the earlier Quadratic trend model...