Analysis the relationship between consumer confidence index and other macroeconomic indices using RBF network

Transcription

1 Analysis the relationship between consumer confidence index and other macroeconomic indices using RBF network Sun Hao ECE539 Instructor: Pro.Yu Hen Hu

2 Introduction: Motivation: Economists are always concern about how people respond to the current economic situations. So they develop the consumer confidence index to measure the people s opinion on current and future situation. They also have many other macroeconomic indices, which measure different section of the current economic situation. But what is the relation between these indices and other index, in other words, which economic factor has the greatest effect on the attitude of consumer is still not clear? Besides, In American, consumption is account for 70% of GDP, which is the main part of economy. The power of consummation is consumers. So both government and investors pay close attention to the consumer s attitude on consumption. Some researchers have shown that consumer confidence is valuable in the prediction of national consummation. If we can find the relation between consumer confidence and other indices, and successfully predict the confidence using these indices, then it will be helpful for us to predict the future consummation. In my approach, I try to use radial basis function neural network to approximate the relation between the consumer confidence index and other indices. Then I will compare my result with multivariable linear regression method. Finally, I will use my model to see the effect of each economic factor on consumer confidence. Background: There are two key macroeconomic indicators describe the attitude of consumer, one is (ICS) consumer sentiment index published by university of Michigan and consumer confidence index published by The Conference Board. These two indices are quite similar. In my approach, I will use the consumer sentiment index by university of Michigan. The other indices I choose is: CPI: Consumer confidence index, which is a very important index measure the current price level. This data is published every month. Unemployment Insurance initial claims: it is published every week, which is more sensitive than the unemployment rate to the current labor market. DJI: Dow Jones Industrial Average Index, which is a general index measure the performance of stock market. Disposable household income: measure how many money people can spend.

3 Data and preprocessing: The data is from the website of Federal Reserve Bank of ST. Louis and Yahoo! Finance. I get the following indices: consumer sentiment index, CPI, UI Claim, unemployment rate, and DJI return. These data is published at least monthly, I get the monthly data from Jan.2005 to Oct I choose this data range since the economic situation and consumer s behavior changes over years. So the relation years ago may be different from now. Actually, I also get the data from 1992 to 2008 and do the training, which is harder to fitting. Then I calculate the monthly change of each index. For some of the index, I calculated 2 nd degree monthly change. The next step is to choose valuable feature. There are so many kinds of indices, some of them may have relation with ICS and others may don t have. So it is important to choose valuable data. My method is to plot the ICS against each other indices to see weather there is any relation I can see from the plot. If it has relation, I will remain it in my feature vector. Otherwise I will not choose it. The result shows that CPI, UI claims both have some extent linear relationship with ICS and DJI index has weaker relationship with ICS. The ICS in current month has stronger linear relationship with the ICS value in previous month. There is not obvious relation between ICS and disposable income and unemployment rate, the reason may be that these two data is not sensitive and accurate enough. The plot is shown below: Notice in my plot, 1 st change means the monthly change, and 2 nd change means the monthly change on monthly change. For example, if the CPI for Jan. is 100, Feb. is 120, March is 130, then the 1 st change for March is = 10 and 2 nd change for March is ( ) ( ) = = 10. Besides, all the ICS 2 nd change data I use are one month after other data. For example, for the following plot, a point may correspond to 2 nd degree change of April and 1 st degree change of CPI in March. In other words, I am doing a prediction problem on ICS(2 nd change) here. CPI(1st) Vs ICS(2nd)

4 CPI(2nd change) Vs. ICS(2nd change) DJI(1st) Vs. ICS(2nd) UI claim(1st) Vs. ICS(2nd)

5 UI claim(2nd) Vs. ICS(2nd) ICS(1st) Vs. ICS(2nd) As we can see, ICS (2 nd change) has linear relation ship with other indices to some extent. Then these selected data are organized as my data set. Which is shown in the appendix.

6 Model construction: Structure: The overall structure of my model is shown below. I will use the value of current month to predict (approximate) the value in next month. I use the MATLAB neural network toolbox to implement the RBF network. The main function I use is newgrnn. newgrnn creates a two layer network. The first layer has radial basis neurons, and calculates weighted inputs with dist and net input with netprod. The second layer has purelin neurons, calculates weighted input with normprod, and net inputs with netsum. Only the first layer has biases. The structure of neural network is shown below[matlab].

7 Training and testing: I divide the whole data into two part, training set and test set. Training set contains 31 samples and testing contains 10 samples. The model will be developed from the training set and then apply to the testing set to see the result. The RBF is quite powerful in approximate a function, a drawback of RBF is that it is doing interpolation locally, so it may not approximate data well if there is not data near by. The spread parameter of newgrnn function plays a role to increase the prediction range. A smaller the spread will give better fitting on the training data, but it may result in over fitting problem and the prediction region may be too small. So I try different parameter of spread. The corresponding mean square errors are listed and plot below: Spread MSE(Training) MSE(testing) Notice that the best fit for the training set is spread 1 and the best for testing set is corresponding to spread 15. So I choose the order 15 to develop model.

8 Result: Model testing: Apply my model to the training set and plot the target curve and my RBF approximation curve the result is shown below: Target RBF Notice that the RBF fit the training curve quite well. Finally I apply my RBF model and multivariable linear regression method to the testing data. The curve I get is shown below: target RBF Mutilvariable linear regression Notice that the RBF network curve (red) can partly approximate the target curve (blue). And compare with the multivariable linear regression (green), it fit better.

9 The mean square error is for RBF, which is better than the for linear regression method. Effect of each factor: Here I try to vary each variable by 20% and see what is the change of the output: Output change CPI(1 st ) CPI(2 nd ) DJI(1 st ) UI(1 st ) ICS(pass value) Conclusion and discussion: 1. The RBF network can be used to predict the value of consumer confidence index, which give better result than the standard multivariable linear regression method. 2. Besides, I try MLP with back propagation learning. The best mean square I can get is , which is larger than (the best testing result of RBF). In other words, RBF perform better in this case than MPL. 3. To predict the ICS value, it is quite useful and important to include the past ICS value. If we only include the other macroeconomics indices as input. The mean square error will increase from to And MSE for the linear regression method will increase from to From the change of each variable, we can see that the CPI 1 st change has the most significant effect on consumer confidence index. The DJI has weaker effect. And the unemployment insurance initial claim has the weakest effect. It makes sciences, since the CPI measure the price level. It affects every consumers and many consumer indeed deicide their consumption plan depend on the price level. For the unemployment condition, it only affects some of the household. And even people lose job for a while, it may still have save in the bank to spending in a short time. So the effect of unemployment rate has relatively little effect on consumer confidence. Done Jones Index has larger effect than the unemployment rate. The reason may be that most people will learn the news about the performance of stock market and some of them are even hold some stock. So the finance market s performance will have great psychological effect on people s opinion of current economic situation. The last input is the past value of ICS. We may treat this input as a measure of the self adjusts ability of macroeconomic. If we have a higher increase of consumer confidence in the last month, it is quite possible to have low value in this month and vise versa.

10 Reference: board.org/economics/consumerconfidence.cfm Tomaso Poggio, Networks for Approximation and Learning, proceedings of the IEEE, vol. 78, No. 9, September 1990 Appendix: My data set: CPI(1st) CPI(2nd) DJI(1st) UI(1st) ICS(1st) ICS(2nd)

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