R Notebook_Priya

library(itsmr) 
library(datasets)
library(forecast)

# Converting the data into a time series object:
deaths_ts = ts(deaths, start=c(1974, 1), frequency=12)

# fitting seasonal model with period of 12 and removing the seasonal component:

deaths_ds = decompose(deaths_ts, type="multiplicative")$random

# fitting a quadratic trend to the deseasonalized data:
trend_deaths = lm(deaths_ds ~ poly(time(deaths_ts), 2, raw=TRUE))

# Subtracting the estimated seasonal and trend components from the original data to obtain the estimated noise:
deaths_noise = deaths_ts - decompose(deaths_ts, type="multiplicative")$seasonal - predict(trend_deaths)

Warning: longer object length is not a multiple of shorter object length

acf(deaths_noise)

# Assuming 'deaths' is your time series data vector

# Step 1: Convert the data into a time series object
deaths_ts <- ts(deaths, start=c(1974, 1), frequency=12)

# Step 2: Perform a multiplicative seasonal decomposition
deaths_decomp <- decompose(deaths_ts, type="multiplicative")

# Step 3: Fit a quadratic trend to the deseasonalized data
# Deseasonalize by dividing the time series by the seasonal component
deaths_deseasonalized <- deaths_ts / deaths_decomp$seasonal
# Create a time variable for the trend model
time_var <- c(1:length(deaths_deseasonalized))
# Fit the trend model
trend_model <- lm(deaths_deseasonalized ~ time_var + I(time_var^2))

# Step 4: Subtract the estimated seasonal and trend components from the original data
trend_values <- predict(trend_model)
# Recompose to get the trend with seasonality
seasonal_trend <- trend_values * deaths_decomp$seasonal
# Calculate the noise
deaths_noise <- deaths_ts - seasonal_trend

# Step 5: Plot the ACF of the noise
acf(deaths_noise)

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Testing for randomness: Box.test(deaths_noise, lag=20, type=“Ljung-Box”) # ## Box-Ljung test ## ## data: deaths_noise ## X-squared = 202.11, df = 20, p-value < 2.2e-16 # Forecasting the data using a default ARIMA model:

deaths_forecast = forecast(deaths_ts, h=24)

# Using the plot() function to create a plot of the original data, and then add the forecasts using lines().

plot(deaths_ts, xlim=c(1974, 1981), ylim=c(3000, 12000), main="Monthly Deaths", xlab="Year", ylab="Number of Deaths")
lines(deaths_forecast$mean, col="blue")
lines(deaths_forecast$upper[,2], col="red", lty=2)
lines(deaths_forecast$lower[,2], col="red", lty=2)

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