I work for an auditing firm and perform time series analysis with reference to the online training("Forecasting Using R" at DataCamp) and the books.

In order to deepen my understanding, I have recalculated various methods myself, but I cannot reproduce the prediction interval of the meanf function.

Perhaps my formula is wrong, but it would be helpful if someone could teach me the correct formula.

# Packages

library(fpp2)

library(zoo)

# Create a data

mydata <- c(10, 20, 30, 40)

# Create a ts object called myts

myts <- ts(mydata, start = c(2019, 1), frequency = 4)

# Create an autoplot

autoplot(myts)

# meanf

fc_mean <- meanf(myts, h = 2)

autoplot(fc_mean) +

scale_x_yearqtr(format = "%Y-%q") +

labs(x = "", y = "")

# SD of Residuals

sd_resid <- fc_mean$model$sd

# Value of Point forecast

pf <- fc_mean$mean[1]

# Culculate the upper of 95% prediction interval

(ans1 <- pf + sd_resid * qnorm(0.975))

# the upper of 95% prediction interval of the model

(ans2 <- fc_mean$upper[3])

# Not identical!

identical(ans1, ans2)

^{Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos}