Extract forecast from an ARIMA with log and difference (R)

I computed AR's models to predict the value of BTC. In order to make the data stationary i have transformed it :

yt=log(BTS_t)
dyt = yt-yt-1 I take the difference of logarithms (interpretable as the growth rate between two consecutive days). However, I want to extract the forcast of the original value of the BTC.

My code is the following :

Construct data

df_byday <- read_excel("C:/Users/33610/Downloads/dfday.xlsx")
df_byday$log <- log(df_byday$Price)
df_byday$LOGdiff1 <- c(0, diff(df_byday$log, lag = 1))
tsBTC2 <- ts(df_byday$LOGdiff1, start=c(2017,01,01), frequency=365)

Estimate :

summary(mod_ar1)
mod_ma1 <- Arima(tsBTC2, order = c(0, 0, 1))
summary(mod_ma1)
mod_ar8 <- Arima(tsBTC2, order = c(8, 0, 0))
summary(mod_ar8)
mod_arma11 <- Arima(tsBTC2, order = c(1, 0, 1))
summary(mod_arma11)

Correct for non-significant coefficients :

mod_ar8fix <- Arima(tsBTC2, order = c(8, 0, 0), fixed=c(NA,0,0,0,0,0,0,NA,NA))
summary(mod_ar8fix)

Forecast (for the transformed data) :

forecast_ar8 <- forecast(mod_ar8fix, h = 5) 
forecast_ar1 <- forecast(mod_ar1, h = 5)
forecast_ma1 <- forecast(mod_ma1, h = 5)

I want to use this forcast to predict the future value of the BTC and avoid the problem of the log and the difference

Thanks you for your helping!

Solution

Build the log and difference into the fitted model, and the forecast() function will take care of it for you.

e.g.,

library(forecast)

price <- ts(df_byday$Price, start = 2027, frequency = 365)
mod_arima011 <- Arima(price, order = c(0, 1, 1), lambda = 0)
forecast_arima011 <- forecast(mod_arima011, h = 5)

The lambda=0 argument specifies a logarithm. See https://otexts.com/fpp2/arima.html for a textbook introduction.

But since you're modelling daily data, you would be better off not using a ts object or the forecast package. Instead, consider tsibble objects with the fable package. See https://otexts.com/fpp3/arima.html.