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# Set the for loop 
for i in range(1,len(monthly_index)):
    print('='*100)
    # Set the current month-end variable
    current_month_end = monthly_index[(i-1)]
    # Set the next month-end variable
    next_month_end = monthly_index[i]

    # Set the span from the previous to the next month end
    span = len(data.loc[current_month_end:next_month_end,:].index)

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from statsmodels.tsa.arima.model import ARIMA

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pip install pandas numpy matplotlib statsmodels yfinance

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pip install pandas statsmodels matplotlib

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S_3 = Df['S_3'].dropna()
S_9 = Df['S_9'].dropna()

# Since S_3 and S_9 are moving averages, we could check their cointegration with the original Close series
close_price = Df['next_day_price']

# Conduct Engle-Granger Cointegration Test between S_3 and Close price
coint_result_3 = coint(S_3, close_price)

# Conduct Engle-Granger Cointegration Test between S_9 and Close price

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# Plot the both buy-and-hold and the strategy cumulative returns
ggplot(data=df_forecasts, aes(x = date)) +
  geom_line(aes(y = var_stra_cum_returns, color="VAR")) +
  geom_line(aes(y = tvp_var_sv_stra_cum_returns, color="TVP-VAR-SV")) +
  geom_line(aes(y = bnh_cum_returns,color="B&H")) +
  geom_line(aes(y = stra_improved_cum_returns, color="Improved TVP-VAR-SV")) +
  ggtitle("Buy and Hold and Strategies' Cumulative Returns") + xlab("Date") + ylab("Returns") + 
  theme(plot.title = element_text(hjust = 0.5, size=25), legend.position="bottom", legend.text = element_text(size=20)) + 
  scale_x_date(date_labels = "%b %y") +
  theme(

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# Create the VAR-based equally-weighted portfolio returns
df_forecasts$var_stra_returns <- rowMeans((df_forecasts[,match(tickers,colnames(df_forecasts))] *
                                        df_forecasts[,match(ticker_var_forecasts,colnames(df_forecasts))]), 
                                      na.rm=TRUE)

# Set the NaN values of the strategy returns to zero
df_forecasts$var_stra_returns[is.na(df_forecasts$var_stra_returns)] = 0.0

# Create the strategy cumulative returns
df_forecasts$var_stra_cum_returns <- exp(cumsum(df_forecasts$var_stra_returns))

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print(paste0(strrep('=',50)))
print(paste0(strrep('=',50)))
print(paste0(strrep('=',50)))
print(paste0('Estimation of TVP-VAR-SV forecasts'))

if (length(initial_iloc_to_forecast<nrow(df_forecasts))!=0) {
  # The for loop to estimate the model each day
  for (i in initial_iloc_to_forecast:nrow(df_forecasts)) {
    
    # Set the current iteration date

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print(paste0(strrep('=',50)))
print(paste0(strrep('=',50)))
print(paste0(strrep('=',50)))
print(paste0('Estimation of basic-VAR forecasts'))

# Check if VAR forecasts have already been estimated
if (length(as.numeric(rownames(tail(subset(df_forecasts, trade_done == 1) ,1))))==0) {
  
  print(paste0(strrep('=',50)))
  print(paste0(strrep('=',50)))

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# Group the data dates by year and month
options(dplyr.summarise.inform = FALSE)
dates <- var_data %>%
  mutate(month = format(date, "%m"), year = format(date, "%Y")) %>%
  group_by(year, month)  %>% summarise(first_dates = first(date))

# Get the first date of Oct-2021
initial_date = subset(dates, (dates$year=='2019') & (dates$month=='01'))$first_dates

# Import the Excel file in case it exists