City Of SugarLand- Help Desk Tickets Time Series Analysis And Prediction
1 Introduction
In today’s fast-paced digital environments, help desk systems play a critical role in managing customer requests, internal support issues, and IT service queries. The ability to efficiently handle and predict ticket volumes is crucial for ensuring timely support and maintaining operational excellence .This analysis focuses on a help desk dataset that contains ticket submissions over multiple years, providing insight into historical trends, seasonality, and anomalies in support requests.
The primary objective of this report is to perform time series analysis on the ticket submission data. By decomposing the data into its core components—trend, seasonality, and residuals—we aim to understand both long-term movements and recurring patterns in ticket volumes. Furthermore, detecting anomalies helps highlight unusual events that may require further investigation, such as service outages or special projects.In this report, we apply time series decomposition and forecasting to help desk ticket data, building on methods discussed in Box, Jenkins, & Reinsel (Box, Jenkins, and Reinsel 2015).
One of the key aspects of this analysis is forecasting future ticket volumes using SARIMA (Seasonal Autoregressive Integrated Moving Average) models. By accurately predicting future ticket volumes, organizations can better allocate resources, optimize response times, and plan for peak periods of support requests. Effective forecasting is not only crucial for improving customer satisfaction but also helps ensure that the help desk is prepared for expected changes in workload.Previous work by Brown & Smith (Brown and Smith 2020) has shown the value of SARIMA forecasting for IT ticket management, which we also explore in this report.
Upcoming sections will delve into the detailed analysis, showcasing how time series methods can be applied to help desk data to uncover insights, detect anomalies, and forecast future trends. This analysis has practical applications for improving operational efficiency, workload planning, and data-driven decision-making.
We will perform the following steps: - Time series decomposition. - Anomaly detection using residuals. - Forecasting future ticket volumes using SARIMA.
# Load necessary libraries
library(ggplot2)
library(forecast)
library(tseries)
library(lubridate)
library(readxl)
# Read the dataset (replace with correct path)
tickets_data <- read_excel("help_desk_tickets.xlsx")
# Ensure 'created_at' is properly parsed
tickets_data$created_at <- as.Date(tickets_data$created_at, format="%Y-%m-%d")
# Time series: count tickets per day
ticket_trends <- as.data.frame(table(tickets_data$created_at))
colnames(ticket_trends) <- c("Date", "Count")
ticket_trends$Date <- as.Date(ticket_trends$Date)
# Create time series object
ticket_ts <- ts(ticket_trends$Count, frequency = 365, start = c(2020, 1))2 Time Series Decomposition
The first step in my analysis was decomposing the time series into three components: Trend, Seasonality, and Residuals (random noise).
\[ X(t) = T(t) + S(t) + R(t) \]
Where: - \(X(t)\) is the observed value at time \(t\), - \(T(t)\) is the trend component, - \(S(t)\) is the seasonal component, - \(R(t)\) is the residual (random) component.
2.1 Observed Component
The “observed” data represents the raw number of tickets over time. It shows daily fluctuations in ticket volumes from 2020 to 2024.
2.2 Trend Component
This shows the long-term movement in the data. The trend in your decomposition shows an increase in ticket volumes over time with some periods of stabilization.
2.3 Seasonality Component
This reveals repetitive patterns (e.g., weekly, monthly). You have seasonality in your data, indicating periodic cycles, likely due to specific patterns in ticket submissions.
2.4 Residuals (Random Component)
These are the irregular fluctuations left after removing the trend and seasonal components.
# Decompose the time series with a yearly seasonality
decomposed_ts <- decompose(ticket_ts)
# Plot the decomposition
plot(decomposed_ts)
The decomposition reveals that our data has strong seasonal patterns and trends. However, the residuals show some irregularities that could indicate anomalies or noise. Analyzing these residuals further helps detect anomalies (such as outliers in ticket volumes), which brings us to the next step.
3 Analyzing Seasonality
Experimented with different seasonal decomposition periods:
3.1 Monthly Decomposition (Period = 30)
Decomposing the data with a 30-day cycle revealed monthly patterns, highlighting fluctuations that recur monthly.
3.2 Yearly Decomposition (Period = 365)
The yearly decomposition showed long-term seasonal changes, identifying patterns that occur annually.
# Monthly decomposition (period = 30)
ticket_ts_monthly <- ts(ticket_trends$Count, frequency = 30, start = c(2020, 1))
decomposed_monthly <- decompose(ticket_ts_monthly)
plot(decomposed_monthly)
# Yearly decomposition (period = 365)
ticket_ts_yearly <- ts(ticket_trends$Count, frequency = 365, start = c(2020, 1))
decomposed_yearly <- decompose(ticket_ts_yearly)
plot(decomposed_yearly)
These seasonal patterns are important because they show repeating cycles. Understanding when ticket volumes are typically high or low can help with workload planning and resource allocation. However, the presence of outliers or anomalies needs to be explored next to ensure the model accounts for them.
4 Anomaly Detection Using Residuals
In this step, we analyzed the residuals to detect anomalies—days where ticket volumes were much higher or lower than expected.
4.1 Residual Plot
The plot of residuals shows random noise after removing the trend and seasonal components. Some values deviate significantly from the mean, indicating anomalies.
4.2 Thresholds for Anomaly Detection
By setting upper and lower thresholds (e.g., two standard deviations away from the mean), you detected points that were considered anomalies.
# Calculate residuals
residuals_ts <- decomposed_ts$random
# Plot residuals
plot(residuals_ts, main = "Residuals of the Decomposed Time Series")
# Set anomaly detection threshold (e.g., 2 standard deviations)
upper_threshold <- mean(residuals_ts, na.rm=TRUE) + 2 * sd(residuals_ts, na.rm=TRUE)
lower_threshold <- mean(residuals_ts, na.rm=TRUE) - 2 * sd(residuals_ts, na.rm=TRUE)
# Identify anomalies
anomalies <- residuals_ts[residuals_ts > upper_threshold | residuals_ts < lower_threshold]
# Plot anomalies
plot(residuals_ts, main = "Anomalies in Residuals")
points(time(anomalies), anomalies, col="red")
abline(h=upper_threshold, col="green", lty=2)
abline(h=lower_threshold, col="green", lty=2)
Anomaly detection helps identify dates when ticket volumes were unusually high or low. This is useful for investigating potential system issues or specific events. After identifying and handling anomalies, forecasting future volumes can provide insights into expected future trends, which is why the next step was forecasting using SARIMA.
5 SARIMA Model Fine-Tuning and Forecasting
The SARIMA (Seasonal ARIMA) model was used to forecast future ticket volumes for the next 6 months.
The ARIMA equation is given as:
\[ \Phi_p(B)(1 - B^d) X_t = \theta_q(B) \epsilon_t \]
where: - \(B\) is the backshift operator, - \(X_t\) is the value at time \(t\), - \(\epsilon_t\) is the error term, - \(\Phi_p(B)\) is the autoregressive polynomial, - \(\theta_q(B)\) is the moving average polynomial.
5.1 SARIMA Forecast
The forecast plot shows the expected ticket volumes based on
historical data. The model uses both seasonal and non-seasonal
components to predict future values.The ARIMA model was fitted using the
forecast package in R (Hyndman and
Khandakar 2008).
5.2 Forecast Plot
The forecast shows stable ticket volumes with periodic fluctuations. The SARIMA model has successfully captured the seasonality and trends in the data to make accurate predictions. The SARIMA model was used to forecast future ticket volumes, based on principles outlined in Hyndman & Athanasopoulos (Hyndman and Athanasopoulos 2018).
# Fit SARIMA model
fit <- auto.arima(ticket_ts, seasonal=TRUE)
# Forecast for the next 6 months
forecast_6months <- forecast(fit, h=180)
# Plot forecast
plot(forecast_6months)
6 SARIMA Residual Diagnostics
To ensure that the SARIMA model accurately captures the patterns in the data, residual diagnostics were performed.
6.1 Residuals Plot
This plot shows the residuals after fitting the SARIMA model. Ideally, residuals should resemble white noise (random scatter around zero).
6.2 ACF Plot
The Autocorrelation Function (ACF) plot shows the correlation between residuals at different time lags. If most points lie within the confidence interval, it means the residuals have no significant autocorrelation, which is a good sign for model fit.
The Autocorrelation Function (ACF) at lag \(k\) can be defined as:
\[ \rho_k = \frac{\sum_{t=1}^{N-k} (X_t - \bar{X})(X_{t+k} - \bar{X})}{\sum_{t=1}^{N} (X_t - \bar{X})^2} \]
where:
- \(\rho_k\) is the autocorrelation at lag \(k\),
- \(X_t\) is the value of the time series at time \(t\),
- \(\bar{X}\) is the mean of the time series,
- \(N\) is the total number of observations.
6.3 Ljung-Box Test
This statistical test checks if the residuals are independently distributed. A p-value greater than 0.05 would suggest that the residuals are independent and the model fits well. In your case, the p-value is slightly below 0.05 (0.0119), indicating a small degree of autocorrelation in the residuals.
The Ljung-Box test statistic can be calculated using the following formula:
\[ Q = N(N + 2) \sum_{k=1}^m \frac{\hat{\rho}_k^2}{N - k} \]
where:
- \(N\) is the sample size,
- \(\hat{\rho}_k\) is the sample autocorrelation at lag \(k\),
- \(m\) is the number of lags being tested.
# Residual diagnostics for SARIMA model
checkresiduals(fit)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(4,1,5)
## Q* = 403.83, df = 342, p-value = 0.0119
##
## Model df: 9. Total lags used: 3517 Final Findings:
7.1 Seasonality and Trends
The data shows strong seasonal patterns, likely driven by repeating cycles of ticket volumes (e.g., daily, weekly, or monthly). Understanding these patterns is essential for planning and resource allocation.
7.2 Anomalies
Several anomalies were detected, suggesting that certain days had unusual ticket volumes. Investigating these anomalies could reveal important operational insights (e.g., outages, high-demand days). Anomalies were detected using residuals based on techniques described by Chandola, Banerjee, & Kumar (Chandola, Banerjee, and Kumar 2009).
7.3 Forecasting
The SARIMA model provides a robust forecast for the next 6 months. It predicts a stable trend with periodic fluctuations, which can be used to anticipate ticket volumes and plan accordingly.
7.4 Model Diagnostics
While the SARIMA model fits the data well, there is slight autocorrelation in the residuals, meaning the model could potentially be improved by adjusting its parameters further.
Overall, my analysis provides valuable insights into historical ticket patterns and future ticket volume forecasts, helping inform decisions related to resource allocation and workload management.
8 Conclusion
In this report, we conducted a comprehensive time series analysis of help desk ticket volumes, applying decomposition techniques to extract trends, seasonality, and residual components. Our analysis revealed strong seasonal patterns and a steady upward trend in ticket submissions, suggesting a consistent increase in workload over time. Anomaly detection using residuals highlighted several outliers, indicating days with unusually high or low ticket volumes, which could correlate to specific events or system outages. Using the SARIMA model, we successfully forecasted future ticket volumes, providing valuable insights for resource planning and operational efficiency. While the model performed well in capturing the seasonality and trend, slight autocorrelation in the residuals suggests potential for further optimization. Overall, this analysis offers actionable insights that can help improve workload management and enhance decision-making for IT support services.
9 References
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