Introduction to SARIMAX

Below is a step‐by‐step workflow—complete with annotated R code snippets—that you can adapt for your time series analysis. It walks you through:

To itemize the steps use * followed by a space as shown below. This will itemize the steps using bullet points.

• Data preparation (time series objects, handling missingness)
• Exploratory analysis (ACF/PACF, seasonality checks)
• Model identification (choosing (p,d,q)(P,D,Q)[s])
• Fitting SARIMAX (with temperature and rainfall as exogenous regressors)
• Generating two‐year forecasts (including future exogenous series)
• Diagnostic checking (residuals, Ljung–Box, forecast accuracy)
• Visualization and manuscript write‐up tips

For ordered list, use numbers for example:

1. Data preparation (time series objects, handling missingness)
2. Exploratory analysis (ACF/PACF, seasonality checks) etc
   • Find mean, median and mode
   • Variance and Standard Deviation
   • ACF/PCF
   • Seasonality checks and the likes

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1. Setup and import data

The first thing we want to do is to load all necessary libraries.

# install.packages(c("forecast","tseries","lubridate","ggplot2"))
library(forecast)
library(tseries)
library(lubridate)
library(ggplot2)

Next, let’s import the data set. You cn use Ctrl + Alt + I to create another cell for chunk of R codes.

#import data
setwd("C:\\Users\\LENOVO\\Desktop\\My Stuff") #set work directory just we do in RScript

df <- read.csv("Zamfara_STATE.csv")

Wonna check few heads?

head(df)

cases_zam <- df$Confirmed.uncomplicated.Malaria[1:108]
plot(cases_zam, type = "l", col = "red", ylab = "Malaria cases", xlab = "Time (in months)", lwd = 3)

#creates date sequence
date <-  seq(as.Date("2015/1/1"), as.Date("2023/12/1"), by = "month")

#create new dataframe
data <- data.frame(cases_zam, date, df$Temperature[1:108], df$Rainfall[1:108])

2. Create time‐series objects

start_year <- year(min(data$date)) 
start_month <-  month(min(data$date))
y_ts <- ts(data$cases_zam, start = c(start_year, start_month), frequency = 12)

x1_ts <-  ts(data$df.Temperature.1.108., start = c(start_year, start_month), frequency = 12)

x2_ts <- ts(data$df.Rainfall.1.108., start = c(start_year, start_month), frequency = 12)

3. Exploratory Analysis

autoplot(y_ts) + ggtitle("Monthly malaria cases")

ggAcf(y_ts) + ggtitle("ACF of Incidence")

ggPacf(y_ts) + ggtitle("PACF of incidence")

ggseasonplot(y_ts, year.labels = TRUE) + ggtitle("Seasonal Plot of Incidence")

Look for:

• Trend vs stationarity
• Seasonal peaks (e.g. rainy vs. dry months)
• ACF/PACF seasonal lags (lag-12, lag-24, …)

Stationarity and Differencing

Test unit-root:

adf.test(y_ts)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  y_ts
## Dickey-Fuller = -3.9584, Lag order = 4, p-value = 0.01384
## alternative hypothesis: stationary

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