The analysis of forming a perfect model for a certain index ---by analsing price of Dow Jones Indexes Abstract One of the important aim for economists is to form a perfect model to forecast the future price trend of a kind of product, it could be indexes, securities or goods, etc. In this essay, we choose Dow Jones Indexes to verify our theory, which has the longest history among all the indexes of the world. While actually, for America, the years of 2011 and 2012 are troubled times, from credit crisis to unemployment protests, from presidential election to the rumor of the end of the world. All these events had different degrees of impact on America economy. We need to see how these will influence our result.
Introduction
Dow Jones Indexes, NASDAQ Indexes, S&P Indexes, the three major indexes in America, reflect different aspects of America economy. Among the three, Dow Jones Indexes has the longest history in the world with a wide range of applications. It is a powerful representation stock price index as the largest and most authoritative in the world. Since the real estate bubble in 2008, America’s economy was in recession and hardy with any significant improvement. As we can see, in 2011 and 2012 these two years, we didn’t hear much good news either, but it seems that European debt crisis, credit crisis, rumor of the end of world or even presidential election could make America even worse. The volatility of Dow Jones Indexes can be used a method to reflect the influence to some extent. In my essay, I will first analysis the basic information it is shown from data, then try to use models to fit the data, finally compare the two models and get conclusion. My data includes 252 observations of daily history price of Dow Jones Indexes in 2011, and 250 observations of daily history price in 2012.

Data analysis
1. Unit root test First, from the unit root test, the result of year 2011 (Table 1.1) and the result of year 2012 (Table 1.2) both prove the data of two years all exist unit root, with t-statistic smaller than all critical values.
Null Hypothesis: Dow has unit root
Exogenous: Constant t-statistics Prob.*
Augmented Dickey-Fuller Test Statistic
-2.494299
0.1180
Test Critical Values
1% level
-3.456302

5% level
-2.872857

10% level
-2.572875

Table 1.1.1
Null Hypothesis: Dow has unit root
Exogenous: Constant t-statistics Prob.*
Augmented Dickey-Fuller test Statistic
-2.050677
0.2652
Test Critical Value
1% level
-3.456514

5% level
-2.872950

10% level
-2.572925

Table 1.1.2

To this point, I rearranged the data from Dow Jones Indexes to log(Dow Jones Indexes), also differenced them once, the results (Table 1.3 and Table 1.4) are as below. It is easy to see that this time both Log(Dow) from year 2011 and 2012 exceed the critical value of 5%, which means they have eliminated the unit root.

Null Hypothesis: Log(Dow) has unit root
Exogenous: Constant t-statistics Prob.*
Augmented Dickey-Fuller test Statistic
-17.43047
0.0000
Test Critical Value
1% level
-3.995189

5% level
-3.427902

10% level
-3.137310

Table 1.1.3
Null Hypothesis: Log(Dow) has unit root
Exogenous: Constant t-statistics Prob.*
Augmented Dickey-Fuller test Statistic
-15.64106
0.0000
Test Critical Value
1% level
-3.996178

5% level
-3.428900

10% level
-3.137411

Table 1.1.4

2. Choose the optimal lag length Then, due to the VAR model, I use information criteria AIC and SC to choose the optimal lag length. The initial set of lag length was 8. The Table 2.1 shows us that there may have two optimal lag length for the data of 2011---6 or1, but Table 2.2 reflects that both AIC and SC information criteria suggest the optimal lag length to be 1.

Lag
AIC
SC
0
-5.162842
-5.248509
1
-7.464301
-7.435636*
2
-7.462065
-7.419067
3
-7.466700
-7.409369
4
-7.472271
-7.400608
5
-7.468359
-7.382363
6
-7.481625*
-7.381296
7
-7.473597
-7.358936
8
-7.470028
-7.341034
Table 1.2.1
Lag
AIC
SC
0
-6.209614
-6.195197
1
-8.655796*