# How can I calculate Conditional expectation using copula

Let X, Y two time series and $$F_{i, \beta_i}$$ the marginal distribution of residual of each time series and beta is vector of their parameter. I studied the dependence between this two series using copula it's a long study but if you want I can put it here. For simplicity, I assume that $$X_t=\rho_1X_{t-1}+\varepsilon_{t,1}$$ and $$Y_t=\rho_2Y_{t-1}+\varepsilon_{t,2}$$
or $$\varepsilon_{t,1} \sim F_{1,\beta_1}$$ and $$\varepsilon_{t,3} \sim F_{2,\beta_2}$$ in the last step in my study I need to calculate the conditional expectation to obtain forecasting value from my model based on copula. When I was reading some articles I found that formula to calculate Conditional expectation \begin{align*} \widehat{X_{T+1,1}}&=E[X_{T+1,1}|, X_{T+1,2}=x_2]\\ &=\int_{0}^{1} xc_{\theta}\{F_{1,\beta_1}(x- \rho_1X_{T}), F_{2,\beta_2}(Y_{T+1}-\rho_2Y_{T})\}\\~~&\times f_{1,\beta_1}(x_1- \rho_2X_{T}) \end{align*} but really I can't get the idea on how can I calculate this in r I will be thankful for any information

Edit: the data is two time series from 1961 to 2018 the first time series is growth rate annual and the second is annual electricity consumption I used copula to obtain the dependence between these two series and construct the model based on copula by these step: 1. Investigate each univariate time series separately, including the assessment of stationarity, time series model identification, and estimation of model parameters. 2. Compute model residuals from the fitted univariate time series model.\ 3. Apply copulas to the model residuals obtained from step 2. 4. Reconstructed time series using the copula
5.forecasting based on this model(I have problem in this step) I can send the data (excel file)to any one give me his email Thank you for your time everyone.

• There are some examples in stats.stackexchange.com/questions/308775/… Commented May 14, 2020 at 12:28
• Thank you for your answer, but still when I implement it in r got some strange result like 0 for all value of x I test it.if you have any idea about forecasting with model based on copula (article, code r or python…) I will be thankful @kjetil b halvorsen Commented May 14, 2020 at 15:31
• Can you please then give some more details---length of the time series, what it represents in the real world. And please include a link to the data. google scholar search Commented May 15, 2020 at 0:14
• Thank you again for your answer I edit my question and I can send you the data if you give me your email @kjetil b halvorsen. Commented May 15, 2020 at 10:54
• You could just link to the data here but my email (sans blanks) is kjetil 1001 at gmail dot com Commented May 15, 2020 at 12:36