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# Week 11: Time Series Analysis
# Kmex Consult - R Data Science Course
# Open in RStudio and run each block with Ctrl+Enter (Cmd+Enter on Mac).
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# Analyzing and forecasting sequential data

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# WEEK 11 OVERVIEW
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# Time series data has one critical difference: observations are DEPENDENT.
# EXAMPLES:
# - Stock prices (today related to yesterday)
# - Weather (today's temp related to yesterday)
# - Sales (seasonal patterns, trends)
# - Traffic (rush hour patterns)
# - Website traffic (daily/weekly seasonality)
# CHALLENGES:
# - Can't randomize or shuffle data
# - Patterns change over time
# - Need special models
# - Requires stationarity for many methods
# COMPONENTS:
# - Trend: Long-term direction
# - Seasonality: Repeating patterns
# - Cycles: Long-term oscillations
# - Noise: Random variation
# THIS WEEK YOU'LL LEARN:
# ✓ Time series decomposition
# ✓ Stationarity testing
# ✓ Exponential smoothing
# ✓ ARIMA models
# ✓ SARIMA (seasonal ARIMA)
# ✓ Forecasting accuracy metrics
# ✓ Cross-validation for time series

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# KEY CONCEPTS
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# STATIONARITY - CRITICAL REQUIREMENT:
# Most forecasting models require stationary data (constant mean, variance, no trend)


library(forecast)
library(tseries)

# Create time series
ts_data <- ts(c(100, 105, 110, 108, 115, 120, 125), frequency=1)

# Test for stationarity
adf.test(ts_data)
# p < 0.05 → stationary

# If non-stationary, difference
ts_diff <- diff(ts_data)
adf.test(ts_diff)
# p now < 0.05 → stationary

# EXPONENTIAL SMOOTHING - SIMPLE FORECAST:


# Simple exponential smoothing
model_ses <- ses(ts_data, h=5)
forecast(model_ses)

# Holt's (with trend)
model_holt <- holt(ts_data, h=5)
forecast(model_holt)

# Holt-Winters (with seasonality)
model_hw <- hw(ts_data, seasonal="additive", h=5)
forecast(model_hw)

# ARIMA(p,d,q) MODELS:


# Auto ARIMA (automatic parameter selection)
library(forecast)
model_arima <- auto.arima(ts_data)
print(model_arima)

# Forecast
forecast(model_arima, h=5)

# Check residuals (should be white noise)
checkresiduals(model_arima)

# ACCURACY METRICS:


# Common metrics
MAE <- mean(abs(actual - predicted)) # Mean Absolute Error
RMSE <- sqrt(mean((actual - predicted)^2)) # Root MSE
MAPE <- mean(abs((actual - predicted)/actual)) * 100 # % error

# Better: scale-independent
library(forecast)
accuracy(predicted, actual)