Forecasting

Introduction to Forecasting Methods

• The session is focused on methods for forecasting, specifically introductory techniques that are simple yet effective for various applications.

• It is highlighted that these methods work well in situations with limited data points or unclear trends in the data.

• These methods will serve as benchmark techniques against complex machine learning forecasting methods, which may also utilize these fundamental approaches.

Agenda Overview

• Time Series Exploration:

  • Understanding your data before building a model or making forecasts, similar to regression analysis.

  • Key components of time series data include:

  • Level

  • Trend

  • Seasonality

  • Noise (which should not be predicted)

• Key Focus Areas:

  • Identifying trends in time series data.

  • Understanding seasonality in time series.

• Forecasting Methods:

  • Introduction to naive forecasting, moving averages, and exponential smoothing.

  • Reference to textbook sections 8.3 for additional insights.

Time Series Components

• Components of time series:

  • Level: The base value around which the time series fluctuates.

  • Trend: The long-term movement in the data, can be upwards or downwards.

  • Seasonality: Regular fluctuations that occur at specific intervals (e.g., monthly).

  • Noise: Random variations that do not follow a discernible pattern.

Understanding the Components

• Noise in time series cannot be predicted, and forecasting methods should focus on identifying and predicting the underlying level, trend, or seasonality.

• Example observed: Straight line level forecasts can be more accurate than forecasts that try to incorporate noise without clear patterns.

Identifying Trends and Seasonality

• Visual Analysis:

  • Analyzing time series visually can help determine the presence of trends and seasonality.

  • Example Products:

  • UK Gross Domestic Product: Acknowledge the upward trend.

  • US Exports of Leather: No clear trend; possible level time series.

  • Ice Cream Sales: Seasonal peaks expected over summer months.

  • Durable Consumer Goods: Notable trends and seasonality.

  • Airline Passenger Data: Observed trends and seasonal effects.

• Automated Trend Detection:

  • Businesses often need to analyze numerous time series simultaneously, making manual visual assessments impractical.

  • Centered Moving Average (CMA): A method used to smooth out time series data, reducing noise to reveal underlying trends.

  • Calculation involves averaging a series of observations and placing this average at the center of the respective time frame.

  • Example Calculation:

  • Average for periods 1, 2, and 3:

    • Given values: 86, 109, 117

    • Calculation: $(86 + 109 + 117) / 3 = 104$

    • The average (104) is placed in the second position of the timeframe.

Moving Averages

• Standard Moving Average:

  • The simple moving average captures a specific number of past observations.

  • Length decision depends on the data's periodicity:

  • Example: Monthly data -> SMA of 12 (for yearly seasonality).

  • Quarterly data -> SMA of 4; Daily data -> SMA of 7; Weekly data -> SMA of 52.

• Moving Averages in Excel:

  • Excel includes functions to calculate moving averages automatically.

  • Manual calculation often requires balancing ends when considering average lengths that are even.

Forecasting Methods Overview

• Naive Forecasting:

  • Definition: The simplest forecasting technique where tomorrow's value is predicted as equal to today's value.

  • Limitations: Sensitive to outliers; forecast can lag behind actual trends.

  • Example Scenario: Forecasting SKU stock in Supply Chain Management.

  • May perform unexpectedly well for sudden level changes, though it cannot filter out noise.

• Average Forecast:

  • Definition: Uses all historical data to give a collective average for predictions.

  • Benefits: Robust to noise and outliers but slow to react to trend changes.

Comparison of Techniques

• Naive vs. Average Forecast:

  • Naive Forecast:

  • Memory: One observation only.

  • Cannot filter noise.

  • Average Forecast:

  • Memory: Long-term based on all observations.

  • Less reactive to recent trends.

• Moving Average Forecast:

  • Takes a few recent observations into account and defines a balance between naive and average methods.

  • Definition: If calculating a moving average for February, the average of the previous three months is used.

Seasonal Effects in Data

• Seasonal effects can be visualized by plotting seasonal data over multiple years to identify patterns.

  • Important to decompose trends before analyzing seasonality to avoid misinterpretation due to overshadowing trends.

Exponential Smoothing

• Exponential Smoothing Formula:

  • ( \hat{y}{t+1} = \alpha yt + (1 - \alpha) \hat{y}_t )

  • Where:

  • (y_t): Actual value today

  • (\hat{y}_t): Forecasted value for today

  • (\alpha): Smoothing constant between [0,1].

Alpha Parameter Control:

• Lower (\alpha) emphasizes historical data (closer to average).

• Higher (\alpha) reacts more to recent observations (closer to naive forecasting).

Final Remarks

• Explore different values of (\alpha) to optimize forecast performance based on the data patterns.

• Training and practice with formulas and methods are highly recommended for exams and practical applications.