library(tidyverse)
library(fpp3)
library(lubridate)
# Create sample Pakistan GDP data (quarterly)
pak_gdp <- tibble(
date = seq.Date(from = as.Date("2000-01-01"),
to = as.Date("2023-10-01"), by = "quarter"),
gdp = 100 * exp(0.015 * 1:length(date)) *
(1 + 0.05 * sin(2 * pi * (1:length(date))/4)) +
rnorm(length(date), 0, 2)
) %>%
as_tsibble(index = date)
# Decomposition
pak_gdp %>%
model(STL(gdp)) %>%
components() %>%
autoplot() +
labs(title = "Pakistan GDP Decomposition",
subtitle = "Trend, Seasonal, and Remainder Components",
y = "GDP (Billions PKR)")EC614: Macroeconomic Forecasting
Lecture 1: Introduction to Macroeconomic Time Series
Prof. Dr. Zahid Asghar
School of Economics, Quaid-i-Azam University
2026-09-14
Course Overview
EC614: Macroeconomic Forecasting
- Focus: Multivariate econometric methods for policy analysis
- Core Topics: VAR, SVAR, Cointegration, VECM, Panel Data
- Tools: R, Python, Real macroeconomic data
- Applications: Central banking, policy transmission, forecasting
“Understanding how economic variables interact over time”
What Makes Macroeconomic Data Special?
Traditional Data Characteristics: - Cross-sectional independence - Fixed relationships - Static analysis
Time Series Properties: - Temporal dependence - Trending behavior - Seasonal patterns - Structural breaks - Cointegration relationships
Key Questions We’ll Answer:
- How do we model economic relationships that evolve over time?
- What happens when monetary policy changes?
- How do external shocks transmit through the economy?
- Can we distinguish temporary from permanent effects?
- How do we forecast in real-time?
The Four Components of Time Series
Every macroeconomic time series can be decomposed into:
1. Trend (Tt) - Long-term direction - GDP growth, inflation trends
2. Seasonal (St) - Regular patterns within year - Agricultural output, energy consumption
3. Cyclical (Ct) - Business cycle fluctuations - Recessions, expansions
4. Irregular (It) - Random shocks - Natural disasters, policy surprises
Decomposition Models:
Additive: Yt = Tt + St + Ct + It
Multiplicative: Yt = Tt × St × Ct × It
Choice depends on whether seasonal fluctuations are constant (additive) or proportional to trend level (multiplicative).
Pakistan’s GDP: A Classic Example
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose
import seaborn as sns
# Create sample Pakistan GDP data
dates = pd.date_range('2000-01-01', '2023-10-01', freq='Q')
trend = 100 * np.exp(0.015 * np.arange(len(dates)))
seasonal = 1 + 0.05 * np.sin(2 * np.pi * np.arange(len(dates)) / 4)
noise = np.random.normal(0, 2, len(dates))
gdp = trend * seasonal + noise
pak_gdp = pd.Series(gdp, index=dates, name='gdp')
# Decomposition
decomposition = seasonal_decompose(pak_gdp, model='additive')
fig, axes = plt.subplots(4, 1, figsize=(12, 10))
decomposition.observed.plot(ax=axes[0], title='Pakistan GDP')
decomposition.trend.plot(ax=axes[1], title='Trend')
decomposition.seasonal.plot(ax=axes[2], title='Seasonal')
decomposition.resid.plot(ax=axes[3], title='Residual')
plt.tight_layout()
plt.show()What We Learn:
- Trend: Pakistan’s GDP shows steady growth with some volatility
- Seasonal: Agricultural effects create regular quarterly patterns
- Cyclical: Business cycle effects embedded in trend-cycle
- Irregular: Policy shocks, external events create noise
Why This Matters: - Understanding components helps design appropriate models - Different components require different forecasting approaches - Policy effects vary by component (temporary vs permanent)
Why Multivariate Methods Matter
The Macroeconomic Reality:
- Economic variables don’t move in isolation
- GDP ↔︎ Inflation ↔︎ Interest Rates ↔︎ Exchange Rates
- System-wide thinking is essential
Univariate Limitations: - Ignores cross-variable relationships - Cannot analyze policy transmission - Misses structural relationships - Poor out-of-sample forecasting
Course Progression:
Weeks 1-5: Univariate foundations - Time series properties - ARIMA models - Stationarity testing
Weeks 6-12: Multivariate core - VAR: System modeling - SVAR: Structural analysis
- Cointegration: Long-run relationships - VECM: Error correction - Panel Data: Cross-country analysis
Exploring Macroeconomic Relationships
library(fredr)
library(patchwork)
# Set FRED API key (you need to register)
# fredr_set_key("YOUR_API_KEY")
# Get US macro data for demonstration
macro_data <- tibble(
date = seq.Date(from = as.Date("2000-01-01"),
to = as.Date("2023-12-01"), by = "month"),
gdp_growth = rnorm(length(date), 2.5, 1.5),
inflation = 2 + 0.5 * sin(2 * pi * (1:length(date))/12) +
rnorm(length(date), 0, 0.8),
interest_rate = 3 + 0.3 * lag(inflation, 1) +
rnorm(length(date), 0, 0.5),
unemployment = 6 - 0.2 * gdp_growth + rnorm(length(date), 0, 0.3)
) %>%
pivot_longer(-date, names_to = "variable", values_to = "value")
# Create dashboard
p1 <- macro_data %>%
ggplot(aes(x = date, y = value, color = variable)) +
geom_line(size = 1) +
facet_wrap(~variable, scales = "free_y", ncol = 2) +
theme_minimal() +
labs(title = "Macroeconomic Indicators Dashboard",
subtitle = "Interconnected movements over time") +
theme(legend.position = "none")
print(p1)import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from datetime import datetime
# Create synthetic macro data
np.random.seed(42)
dates = pd.date_range('2000-01-01', '2023-12-01', freq='M')
n = len(dates)
# Generate correlated macroeconomic variables
gdp_growth = np.random.normal(2.5, 1.5, n)
inflation = 2 + 0.5 * np.sin(2 * np.pi * np.arange(n) / 12) + np.random.normal(0, 0.8, n)
interest_rate = 3 + 0.3 * np.roll(inflation, 1) + np.random.normal(0, 0.5, n)
unemployment = 6 - 0.2 * gdp_growth + np.random.normal(0, 0.3, n)
macro_df = pd.DataFrame({
'GDP Growth': gdp_growth,
'Inflation': inflation,
'Interest Rate': interest_rate,
'Unemployment': unemployment
}, index=dates)
# Create subplot dashboard
fig, axes = plt.subplots(2, 2, figsize=(15, 10))
axes = axes.ravel()
for i, col in enumerate(macro_df.columns):
axes[i].plot(macro_df.index, macro_df[col], linewidth=2)
axes[i].set_title(f'{col}', fontsize=14, fontweight='bold')
axes[i].grid(True, alpha=0.3)
plt.suptitle('Macroeconomic Indicators Dashboard', fontsize=16, fontweight='bold')
plt.tight_layout()
plt.show()
# Correlation heatmap
plt.figure(figsize=(8, 6))
correlation_matrix = macro_df.corr()
sns.heatmap(correlation_matrix, annot=True, cmap='RdBu_r', center=0,
square=True, cbar_kws={'label': 'Correlation'})
plt.title('Macroeconomic Variables Correlation Matrix')
plt.tight_layout()
plt.show()Cross-Variable Relationships:
- Phillips Curve: Inflation ↔︎ Unemployment (negative correlation)
- Taylor Rule: Interest rates respond to inflation
- Okun’s Law: GDP growth ↔︎ Unemployment (negative correlation)
Why Correlation Matrices Matter: - Reveal contemporaneous relationships - Guide VAR model specification - Identify potential cointegration relationships - Inform structural identification in SVAR models
Data Sources for Macroeconomic Analysis
Pakistan Data Sources:
- State Bank of Pakistan (SBP)
- Monetary policy rates
- Exchange rates
- Money supply (M0, M1, M2)
- Banking sector data
- Pakistan Bureau of Statistics (PBS)
- GDP components
- CPI, inflation indices
- Employment statistics
- Industrial production
- Ministry of Finance
- Fiscal indicators
- Government debt
- Budget data
International Sources:
- Federal Reserve Economic Data (FRED)
- High-quality, API access
- 800,000+ time series
- World Bank Open Data
- Cross-country panels
- Development indicators
- IMF Data
- International Financial Statistics
- Balance of payments
- OECD Statistics
- Advanced economy indicators
Accessing Data Programmatically
# Multiple data source packages
library(fredr) # FRED data
library(WDI) # World Bank
library(IMFData) # IMF
library(OECD) # OECD
library(readxl) # Local files
# FRED example
fredr_set_key("YOUR_API_KEY")
us_gdp <- fredr(series_id = "GDP")
# World Bank example
pak_indicators <- WDI(
country = "PK",
indicator = c("NY.GDP.MKTP.CD", "FP.CPI.TOTL.ZG"),
start = 2000,
end = 2023
)
# Local Pakistan data
sbp_data <- read_excel("data/sbp_monetary_data.xlsx")
# Combine and clean
macro_panel <- pak_indicators %>%
left_join(sbp_data, by = "year") %>%
mutate(across(where(is.numeric), ~na_if(., ""))) %>%
drop_na()import pandas as pd
import yfinance as yf
import pandas_datareader as pdr
from fredapi import Fred
import wbdata
import quandl
# FRED API
fred = Fred(api_key='YOUR_API_KEY')
us_gdp = fred.get_series('GDP', start='2000-01-01')
# World Bank
pak_gdp = wbdata.get_data('NY.GDP.MKTP.CD', country='PK')
# Yahoo Finance for financial data
stock_data = yf.download('^KSE100', start='2000-01-01')
# Quandl for additional sources
quandl.ApiConfig.api_key = "YOUR_API_KEY"
commodity_data = quandl.get("OPEC/ORB", start_date="2000-01-01")
# Local files
sbp_data = pd.read_excel('data/sbp_monetary_data.xlsx')
# Merge datasets
macro_data = pd.merge(pak_gdp, sbp_data, on='date', how='outer')
macro_data = macro_data.dropna()Data Collection Guidelines:
- Version Control: Track data vintage and revisions
- Documentation: Metadata for each series
- Frequency Alignment: Monthly, quarterly conversions
- Missing Values: Interpolation vs exclusion
- Seasonal Adjustment: When and how to apply
Common Pitfalls: - Using different seasonal adjustment methods - Mixing real vs nominal variables - Ignoring data revisions - Inconsistent frequencies - Missing structural breaks
Course Roadmap: From Simple to Complex
Phase 1: Foundations (Weeks 1-5) - Time series properties - Stationarity and unit roots
- ARIMA modeling - Structural breaks
Phase 2: Multivariate Core (Weeks 6-12) - VAR: System relationships - SVAR: Structural identification - Cointegration: Long-run relationships - VECM: Error correction dynamics - Panel Data: Cross-country analysis
Phase 3: Modern Methods (Weeks 13-15) - Machine learning integration - High-dimensional forecasting - Nowcasting techniques - Policy applications
Assessment Strategy: - 25% Midterm (Traditional methods) - 30% Final (Comprehensive) - 20% Labs (Hands-on practice) - 20% Research project - 5% Participation
Next Week Preview: Time Series Properties
What We’ll Cover in Lecture 2:
Theoretical Concepts: - Stationarity (weak vs strong) - Autocovariance functions - White noise processes - Random walks vs trend-stationary
Practical Skills: - ACF and PACF interpretation - Unit root testing - Data transformation techniques
Preparation: - Read: FPP3 Chapters 2-3, Enders Ch. 2 - Install: Required R/Python packages - Download: Practice datasets from course website - Lab: Stationarity testing with Pakistan macro data
Key Question: “How do we know if our data is suitable for modeling?”
Software Setup and Resources
Required Software:
R Environment:
Python Environment:
Key Resources:
- Course Website: All slides, data, assignments
- Textbooks: FPP3 (free online), Enders (library)
- Software Help: Office hours, online tutorials
- Data Sources: FRED, World Bank APIs
- Discussion Forum: Course Q&A platform
Office Hours: Tuesday & Thursday 2-4 PM
Questions and Discussion
Key Takeaways from Today:
- Macroeconomic time series have unique properties requiring specialized methods
- Decomposition reveals trend, seasonal, cyclical, and irregular components
- Multivariate methods are essential for understanding economic systems
- We’ll progress from univariate foundations to advanced policy applications
- Both R and Python provide excellent tools for time series analysis
Coming Up:
- Next Lecture: Time series properties and stationarity
- Lab Session: Hands-on data exploration
- Assignment 1: Due next Friday
- Reading: FPP3 Ch. 2-3
Questions?
Contact: zasghar@qau.edu.pk
References
Primary Textbooks: - Hyndman, R.J., & Athanasopoulos, G. (2021). Forecasting: principles and practice, 3rd edition. OTexts. - Enders, W. (2014). Applied Econometric Time Series, 4th edition. Wiley.
Key Papers: - Sims, C.A. (1980). Macroeconomics and reality. Econometrica, 48(1), 1-48. - Engle, R.F., & Granger, C.W.J. (1987). Co-integration and error correction. Econometrica, 55(2), 251-276.
Software Documentation: - R: fpp3.com, CRAN Task View: Time Series - Python: statsmodels.org, pandas.pydata.org
EC614: Macroeconomic Forecasting | QAU