• The objective is to forecast GDP growth using Time Series Analysis.
• We’ll use synthetic GDP data for illustration.
• Tools: R, ggplot2, forecast, plotly.

This section outlines the R packages crucial for our GDP growth forecasting analysis:

1. ggplot2: Used for creating detailed static visualizations of GDP trends.
2. forecast: Provides automatic ARIMA modeling for time series forecasting.
3. plotly: Enables interactive graphing for an engaging data exploration experience.
4. tseries: Offers tools for preliminary time series analysis and testing.

• To illustrate the process of forecasting GDP growth, we generate synthetic GDP data, aiming to mimic real-world economic fluctuations.
• This synthetic dataset spans from 2000 to 2024, on a quarterly basis, creating a realistic timeline for analysis.
• The generated GDP values, representing a hypothetical country’s economic output over time.
• This dataset serves as a basis for exploring time series analysis techniques, specifically focusing on how to forecast future GDP growth based on historical data.

• Visualizing the synthetic GDP data over time helps understand its trend.

• We apply ARIMA (AutoRegressive Integrated Moving Average) modeling to forecast future GDP growth, utilizing the historical patterns embedded within our synthetic GDP data.
• ARIMA models are particularly useful in time series forecasting because they can capture various stochastic trends in the data, making them ideal for economic data analysis.
• The auto.arima() function in R simplifies the model selection process by automatically determining the optimal parameters (p, d, q) that best fit the historical data, ensuring the most accurate forecasts possible.
• We selected an 8-quarter horizon for our forecasts to provide short to medium-term economic insights, which are crucial for policy planning and business strategy.

• The forecasted GDP growth for the next 8 quarters is visualized below.

• This slide showcases the R code used for creating a GDP growth visualization with ggplot2, demonstrating practical application of the concepts discussed.

ggplot(gdp_data, aes(x = time, y = gdp)) + 
  geom_line(color = "hotpink1") + 
  ggtitle("Synthetic GDP Growth Over Time") + 
  xlab("Year") + 
  ylab("GDP")

• An interactive visualization of forecasted GDP growth using Plotly enhances the presentation and interpretation of results, providing a clear and engaging view of future GDP trends.

The ARIMA model is defined by three parameters: (p, d, q).

• \(p\): Autoregressive order
• \(d\): Degree of differencing
• \(q\): Moving average order

The model can be mathematically represented as:

\[ARIMA(p, d, q): (1 - \sum_{i=1}^{p} \phi_i L^i)(1 - L)^d X_t = (1 + \sum_{i=1}^{q} \theta_i L^i) \varepsilon_t\]

Where: - \(L\) is the lag operator - \(\phi_i\) are the parameters of the autoregressive part - \(\theta_i\) are the parameters of the moving average part - \(\varepsilon_t\) is white noise.

• Time Series Analysis is a powerful tool for economic forecasting.
• Our ARIMA model provides a glimpse into future GDP trends.
• Tools like ggplot2 and Plotly enhance the presentation and interpretation of results.