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Questions and Answers

What is the primary purpose of forecasting in the context of time series analysis?

  • To identify historical trends without future implications
  • To manipulate past data to suit business needs
  • To predict future behaviors based on historical patterns (correct)
  • To predict the exact values of future data points

Which characteristic defines a time series as equally spaced?

  • Data points can vary in the interval they are measured
  • The measurement must be in different units over time
  • The data points must be collected on weekends only
  • There is a consistent time interval between consecutive data points (correct)

What is a common application of time series forecasting in supply chain management?

  • Predicting employee performance over the prior year
  • Determining when to reorder raw materials (correct)
  • Analyzing customer satisfaction scores
  • Calculating the conversion rates of marketing campaigns

Which of the following is NOT a component typically accounted for in time series data?

<p>Stationarity (D)</p> Signup and view all the answers

Why is it important to account for patterns like autocorrelation in forecasting?

<p>It allows for better predictions based on past behaviors (B)</p> Signup and view all the answers

What does 'prediction is very difficult, especially if it's about the future' imply about forecasting?

<p>Forecasts depend heavily on the quality of historical data (C)</p> Signup and view all the answers

Which aspect of time series data allows for the quantification of patterns over time?

<p>The consistent interval of time between measurements (B)</p> Signup and view all the answers

What is a critical limitation of relying solely on past data for forecasts?

<p>Historical data might not always represent future trends (C)</p> Signup and view all the answers

What defines the seasonality in a time series?

<p>Repetitive behavior at fixed seasonal periods. (A)</p> Signup and view all the answers

In the context of seasonal dummy variables, what does a dummy variable represent?

<p>An indicator variable for a specific time point. (D)</p> Signup and view all the answers

Which equation represents seasonal differencing in a time series?

<p>$Y_t = Y_{t-S} + TREND_t + IRREGULAR_t$ (A)</p> Signup and view all the answers

In a time series with $S$ seasons, how many dummy variables are there?

<p>One for each season. (C)</p> Signup and view all the answers

What is represented by the equation $Y_t = f(T_t, S_t, X_t, E_t)$ in the Universal Time Series Model?

<p>The combined effect of trend, seasonal, input, and irregular components. (C)</p> Signup and view all the answers

What type of data would use the dummy variable notation $I_{MON}$ for January?

<p>Monthly data. (B)</p> Signup and view all the answers

Which of the following is NOT a component removed when analyzing the irregular component of a time series?

<p>Dummy variables. (B)</p> Signup and view all the answers

When performing seasonal differencing, which of the following expressions is correct for a monthly time series?

<p>$ riangle MY_t = Y_t - Y_{t-12}$ (A)</p> Signup and view all the answers

What does the symbol $Y_t$ in the Universal Time Series Model represent?

<p>The outcome or measurement at time $t$ (D)</p> Signup and view all the answers

Which of the following is a characteristic of a deterministic trend?

<p>It can be predicted perfectly. (B)</p> Signup and view all the answers

What is the formula for a linear trend in a time series?

<p>$Y_t = eta_0 + eta_1\cdot t$ (C)</p> Signup and view all the answers

What is the purpose of differencing in time series analysis?

<p>To convert a random walk into a stationary series. (B)</p> Signup and view all the answers

Which type of trend component includes random variations and cannot be predicted perfectly?

<p>Stochastic trend (C)</p> Signup and view all the answers

In the context of time series, what does seasonality refer to?

<p>Recurrent patterns at specific intervals in the data (A)</p> Signup and view all the answers

What is the equation for a random walk with drift?

<p>$Y_t = \mu + Y_{t-1} + E_t$ (D)</p> Signup and view all the answers

Which of the following statements about first differences is true?

<p>It provides a way to analyze stochastic trends. (C)</p> Signup and view all the answers

Flashcards

Equally Spaced Time Series

A time series where data points are recorded at consistent intervals.

Universal Time Series Model

A model for time series data, encompassing trend, seasonality, inputs, and random error.

Time Series Trend

A systematic pattern of change in a time series (deterministic or stochastic).

Deterministic Trend

A trend that can be perfectly predicted, showing no random variation.

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Linear Trend

A time series trend that follows a straight line.

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Random Walk

A stochastic trend where the current value depends only on the previous value, plus random error.

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Seasonality

A repeating pattern of change within a time series, related to specific seasons or periods.

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Differencing

A method to remove the component of a random walk time series to make it stationary

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Time Series

A sequence of data points collected over time at equal intervals, with the same type of measurement.

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Forecasting

Predicting future behavior of a variable, considering patterns in past data.

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Time Series Characteristics

Properties of time series data, including equally spaced time intervals and the same measurement type.

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Forecasting Models

Techniques used to predict future values in a time series based on patterns in prior data.

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Statistical Time Series

An ordered set (sequence) of data, often with constant time intervals between data points.

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Business Applications of Forecasting

Using forecasts to make decisions in various business areas, such as inventory management, demand planning, and pricing strategies.

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Forecast Limitations

Forecasts are not perfect; past data may not perfectly predict the future due to changes in circumstances.

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Seasonal Variation

Repetitive patterns in data, occurring at known seasonal periods, often influenced by celestial bodies like the sun and moon.

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Seasonal Factors

Factors that repeat regularly after a fixed number of time units (e.g., quarters for quarterly data).

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Dummy Variable

An indicator variable taking value 1 for a particular time point and 0 for all other points.

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Seasonal Dummy Variables

Separate dummy variables for each season in a time series. Used to account for seasonal patterns.

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Seasonal Differencing

Calculating the difference between a data point and the same point from a fixed time period ago (e.g., previous quarter).

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Irregular Component

The remaining component in a time series after accounting for trend, seasonal, and input effects. Represents randomness, or unexplained fluctuations.

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Time Series Analysis

Analyzing data points collected over time to understand patterns, predict future values, and identify influential factors like seasonality.

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Study Notes

Forecasting Time Series Overview

  • Course name: DSBA 6211
  • Instructor: Dr. Zhao
  • Topics covered: Introduction, Time Series Characteristics and Components, Forecasting Models
  • Forecasting aims to predict future behavior of variables, accounting for internal structures like autocorrelation, trends, and seasonality.
  • Time series data is used for forecasting.

Introduction to Forecasting

  • Forecasting is a form of predictive modeling.
  • Aims to predict outcome variables (e.g., sales, buy/no buy).
  • Critical to account for internal time-related patterns (like autocorrelation, trends, seasonality).
  • Time series data encompasses the information collected over time using equally spaced time intervals.
  • Time-series data allows for the visualization and quantification of patterns over a time interval.
  • Enables forecasting for future points based on past behavior.

Business Applications

  • Inventory Management: Should you use shelf space for more peanut butter or salsa? Will putting an item on sale decrease demand?
  • Demand Management: What time of day produces peak server demand?
  • Supply Chain Management: When should you reorder raw materials?
  • Pricing: What are pricing trends in the past quarter compared to the previous three years?

Caution

  • Prediction is challenging, especially about the future (Nils Bohr).
  • Forecasts are only as good as the included past data.
  • History is not a perfect predictor of the future.

Time Series Characteristics and Components

  • A statistical time series is a sequence of indexed numbers (dates or other numerical values).
  • Many business time series are equally spaced (same interval between consecutive points).
  • Equally spaced time series can have missing values.

The Universal Time Series Model

  • Yt = f(Tt, St, Xt, Et)
  • Components:
    • Trend (T): long-term movement
    • Seasonal (S): recurring patterns (e.g., monthly, quarterly)
    • Input (X): external factors influencing the time series
    • Error (E): random fluctuations

Airline Passengers 1994-1997 Series Plot

  • Shows a rise in airline passengers between 1994 and 1997.

Time Series Trend

  • Trend represents a deterministic function of time.
  • Stochastic components are subject to random variation.
  • Deterministic components exhibit no random variation and can be predicted perfectly.
  • Examples of deterministic trend functions: linear, curvilinear, logarithmic, exponential.

Deterministic Trend Models

  • Linear Trend: Yt = β0 + β1t
  • Quadratic Trend: Yt = β0 + β1t + β2t²

Stochastic Trend Models

  • Random Walk: Yt = Yt-1 + Et
  • Random Walk with Drift: Yt = μ + Yt-1 + Et

Accommodating Stochastic Trend: Differencing

  • First difference of Random Walk process: Yt - Yt-1 = Et
  • ΔYt = Yt - Yt-1

Accommodating Seasonal Components

  • Trigonometric functions (sine waves)
  • Seasonal dummy variables/indicator variables
  • Seasonal differences (Box-Jenkins modeling)

Dummy Variables

  • Indicator variable.
  • Takes value 1 for a specific time point, 0 otherwise.
  • Used to represent seasonal variations.

Seasonal Dummy Variables

  • For a series with S seasons, there are S dummy variables.
    • Monthly: IJAN, IFEB, ..., IDEC
    • Daily: ISUN, IMON, ..., ISAT
    • Quarterly: IQ1, IQ2, IQ3, IQ4

Stochastic Seasonal Functions: Seasonal Differencing

  • Express current value as a function involving value S time units prior.
  • Yt = Yt-S + Trend + Irregular

The Irregular Component

  • Remains after removing trend, seasonal, and input effects.
  • Represents forecast error.

Additive Decomposition of the Airline Data

  • Breaks down the time series into trend, seasonal, and irregular components.

Forecasting Models

  • Regression-based: Uses suitable predictors to capture trends and seasonality.
    • Examples: Linear, Quadratic trend, Additive seasonality
  • Smoothing methods:
    • Moving average: Uses past t periods to predict t+1
      • Simple: average of past n periods;
      • Weighted: Past periods have different weights (more recent periods usually have higher weights).
    • Exponential smoothing: Emphasizes most recent values. Smoothing constant (α) determines the degree.
  • Autoregressive Integrated Moving Average (ARIMA) Models:
    • Uses lagged values of the dependent variable and/or random disturbance term as predictors.
    • Relies heavily on autocorrelation patterns in the data.

Model Performance Evaluation

  • Forecast error measures:
    • MA (mean error), RSMA (root mean squared error), MAE (mean absolute error)
    • MPE (mean percentage error)
    • MAPE (mean absolute percentage error)
    • Scaling errors based on training MAE; MASE (mean absolute scaled error)

Event Variable Improvements to Accuracy

  • Event variables (like promotions, policy changes) help accommodate disruptions in time series data.
  • Primarily used to modify intercepts of models.
  • Expressed as binary variables (0 or 1).

Event Variable Creation

  • Event variables are created by adding a 0-1 (binary) column to existing data, specifying events.

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