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For my Master thesis I have to perform the DCC-GARCH model to examine the correlation between real estate house prices and the stock market. I tested the data for normality (both not normal) and stationarity (both not stationary) and variance ratio test (was significant).

I used the log function because of the non-normality and took the first difference. After this, the real estate house prices were still not stationary, so I took the second difference which resulted in stationary data. The stock market data was stationary after taking the first difference, but I think I need to take the second difference as well in order to use it for the DCC-GARCH model.

The code I used for the DCC model is:

#perform DCC
model1=ugarchspec(mean.model = list(armaOrder=c(0,0)),variance.model = list(garchOrder=c(1,1),model="sGARCH"),distribution.model = "norm")
modelspec=dccspec(uspec = multispec(replicate(2,model1)),dccOrder = c(1,1), distribution = "mvnorm")
modelfit=dccfit(modelspec,data=(data.frame(ts_nominal,ts_share)))
modelfit

I'm not sure if I took the right steps to perform this analysis or if my code is even correct. Compared to other papers, I find it strange that only 3 parameters are significant and that alpha1 for stocks and dcca1 are almost equal to 1.

Can anyone help me with this?

Update: Further Research

I have proceeded by taking the log return of both the property price index and stock price index. Then I used the diff() function, resulting in both time series being stationary. The results, however, are barely different than the last results I showed in the post.

Distribution         :  mvnorm
Model                :  DCC(1,1)
No. Parameters       :  11
[VAR GARCH DCC UncQ] : [0+8+2+1]
No. Series           :  2
No. Obs.             :  130
Log-Likelihood       :  502.7599
Av.Log-Likelihood    :  3.87 

Optimal Parameters
-----------------------------------
                   Estimate  Std. Error     t value Pr(>|t|)
[ts_prop].mu       0.000547    0.003082    0.177488 0.859125
[ts_prop].omega    0.000011    0.000072    0.156417 0.875704
[ts_prop].alpha1   0.349696    0.649448    0.538451 0.590266
[ts_prop].beta1    0.649304    0.387195    1.676944 0.093553
[ts_share].mu      0.000031    0.008641    0.003615 0.997116
[ts_share].omega   0.000004    0.000007    0.561343 0.574564
[ts_share].alpha1  0.000000    0.000673    0.000009 0.999993
[ts_share].beta1   0.999000    0.000882 1132.157095 0.000000
[Joint]dcca1       0.000000    0.000007    0.000353 0.999719
[Joint]dccb1       0.895265    0.119982    7.461638 0.000000

Information Criteria
---------------------
                    
Akaike       -7.5655
Bayes        -7.3229
Shibata      -7.5784
Hannan-Quinn -7.4669

Elapsed time : 0.909425

The next step in our analysis is to apply linear regression to see which determinants (like the long term interest rate) have a significant effect on the dynamic correlation between the property return time series and stock return time series. For this, I extracted the dynamic correlations from the DCC-GARCH model, but as you can see in the graph 'fcor', these correlations all have the same value of 0.133784 with minimal changes.

mod1=lm(fcor~long)
> summary(mod1)

Call:
lm(formula = fcor ~ long)

Residuals:
            Min              1Q          Median              3Q             Max 
-0.000000010205 -0.000000003962 -0.000000001022  0.000000004495  0.000000019842 

Coefficients:
                   Estimate      Std. Error       t value             Pr(>|t|)    
(Intercept) 0.1337839573855 0.0000000005038 265555616.311 < 0.0000000000000002 ***
long        0.0000000045540 0.0000000016445         2.769              0.00646 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.000000005664 on 128 degrees of freedom
Multiple R-squared:  0.05652,   Adjusted R-squared:  0.04915 
F-statistic: 7.669 on 1 and 128 DF,  p-value: 0.006455

I also performed regression on other determinants with all having a significant effect on the dynamic correlations. Can someone explain to me why the dynamic correlations barely change and why this has an effect on the linear regression result?

DCC results

Original Nominal Property Index

Original Share Price Index

Property Price with single difference and log

Share Price with single difference and log

Dynamic Correlations

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  • $\begingroup$ I would think twice (or more times) before differencing twice. Usually no more than one difference is warranted. Could you include a plot of the original time series (and perhaps of diff(log(...)) with a single difference)? Also, what do you mean by variance test? Also, next time consider pasting the R output as text, not as picture. $\endgroup$
    – Richard Hardy
    Commented Apr 13, 2023 at 11:21
  • $\begingroup$ Hi @RichardHardy Thank you for your comment. I added the plots to my post. My apologies for the picture, it is my first time using this platform and was not able to implement the results as text. I took advice from several videos online and one proposed to perform the variance ratio test. Since my background in statistics is not that strong, I also implemented this test. $\endgroup$
    – Jan-Willem van Boven
    Commented Apr 13, 2023 at 20:10
  • $\begingroup$ The first time series is a bit unfortunate. diff(log(.)) appears nonstationary, but it does not seem to have a unit root, and thus taking another difference is probably not an adequate measure. In this model, I would perhaps just use the diff(log(.)) as is, even if it is nonstationary. But I do not have a solid defense of either choice. The problem is that the model is inadequate in either case due to the first series exhibiting some form of structural change. $\endgroup$
    – Richard Hardy
    Commented Apr 14, 2023 at 6:53
  • $\begingroup$ Hi @RichardHardy, I proceeded with my research by calculating the log return of both the property price index and stock price index and after using the diff() function, both time series appear to be sationary. I then proceeded with linear regression, but the results are not realistic as i explained in the post after "Further research". Could you also give me some advice on this? $\endgroup$
    – Jan-Willem van Boven
    Commented Apr 23, 2023 at 9:38
  • $\begingroup$ I updated the formatting of your post. Note the formatting of the code using ```r instead of indenting the code as you had done before. Regarding the results, I have only taken a casual look. If the cond. correlation is essentially constant over time (as the DCC results suggest), it does not make much sense trying to analyze the variation; the results, whatever they are, hardly tell us anything. $\endgroup$
    – Richard Hardy
    Commented Apr 23, 2023 at 9:45

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