Reviewer Forecasting and Time Series PDF

Time Series Omega (ω): This represents a particular condition or scenario. Imagine omega as different possible  Is an ordered sequence of observations...

Time Series Omega (ω): This represents a particular condition or scenario. Imagine omega as different possible  Is an ordered sequence of observations situations, like different rolls of a dice.  It is a set of numerical data (univariate/multivariate) obtained at a t (time): This is the specific moment you're looking regular time intervals at. It could be a particular second, minute, hour, etc.  A time series is simply a sequence of data Random Variable at Fixed Time (Z(omega, t) points recorded over time. with fixed t): If you freeze time at a particular  is used to understand past behavior, predict moment (t), Z(omega, t) becomes just a random future trends, or explore relationships value that could vary depending on the condition between different variables over time. (omega). Contains information for analysts who wants Sample Function or Realization: Now, if you fix to: the scenario (omega) and watch how the random  Develop/estimate a model of the process value Z(omega, t) changes over time (t), you're underlying the time series. looking at a "sample function" or a "realization." -Analysts want to create a model (a This is like watching one possible path or outcome mathematical way of explaining) for over time. how the time series data behaves over  A stochastic process is a way to model time. random events happening over time. If  Forecast behavior of the process. you look at one specific moment, you'll -They want to use this model to make see a random value. If you watch how it predictions about what will happen in changes over time under one specific the future based on the time series data. scenario, that's called a sample function  Develop a model of the relationship or realization. between various time series. -Analysts might want to explore how Realization different time series (like sales over  The observed data set. time, stock prices, etc.) relate to each  It is a subset of the possible data other by building a model that connects produced by a process. them.  is just the actual data you observe from  Forecast the effect of movement in one the process. It’s like recording the or more time series over another. outcomes from multiple dice rolls. -they want to forecast how changes in one time series (like an increase in Model interest rates) might impact another time  is a representation of the mechanism that series (like stock market prices). generated the data. Example of Time Series  is a mathematical way to describe the process that produced your data. It's like Time plot or historical plot finding a formula that explains the data you  Plot of a time series over time observed. Stochastic Process Purpose of building models for time series  This is a mathematical concept where  To understand and describe the mechanism values are random but indexed over time that generated the data. (or another dimension). Imagine rolling -Figure out how the data was generated. a dice over time; each outcome is  To forecast values random, but they occur in a sequence. -Predict future values.  To optimize the response of a variable of Stochastic Process: Think of this as a collection of interest. random events that happen over time. These events -Make better decisions based on the data, can change randomly, and they're tracked or such as maximizing profits or minimizing indexed by time (t). costs. Z(omega, t): This is just a fancy way of saying "the  To assist in the formulation of policies random event or value at a specific time (t) and -Help make decisions in areas like under a specific condition (omega)." economics or resource management. Description and understanding if the mechanism -forecasting helps in making decisions today that generated the data that will benefit you in the future.  Vital inputs in the decision-making 1. Descriptive analysis of the data process of -describe your data -This is about looking at your data closely to -Farmers: Helps in planning what crops to plant see what it can tell you. Think of it as and when, based on expected weather conditions or getting a good understanding of the basic market demand. patterns, trends, and behaviors in the data -Development Planners: Assists in planning without making any assumptions. programs or promotions based on future trends. 2. Build models that describe the data and which test the statistical significances or -Policy/Decision Makers: Aids in making patterns observed in the data. decisions about things like importation or market -After you understand the data, the next step interventions by predicting future economic is to create mathematical formulas (models) conditions. that explain what you see. These models help to confirm if the patterns you noticed in Note: the data are statistically significant, meaning they are not just random but have some  Forecasting is not "Trending": underlying reason. o This means that a forecast is an estimate, not a certainty. It's not just Policy Analysis/Optimization about following current trends but  Build models which analyze the effect of using data to make informed predictions. certain factors on some series of interest and  Quality of Forecast: finding ways of optimizing the value of the o A good forecast is usually tested on series of interest. data that wasn’t used to create the -it involves using models to see how model. This helps to see how different factors (like interest rates, weather, accurate the forecast might be in the or prices) influence the data series you're real world (this is what "out-of- interested in. sample" means). -Once you know which factors affect your data, you can use this knowledge to improve Categories of Time Series Models outcomes. Structural Models Forecast  Use of other time series to study the series of  Anticipated levels interest -predicting what the future values of your  Used for long term data might look like.  You can use it in succeeding years  Prognasis of what will happen in the  Structural models are often used for long- future. term forecasting because they incorporate -making predictions or forecasts about future broader influences that affect the time series events based on the data you have. over a longer period.  Early warning of future scenario Nonstructural Models -involves predicting potential future events so you can prepare in advance.  Use only the history or past values of the  Movements of leading indicators series of interest explain and forecast its -Leading indicators are data points that can behavior. predict future trends. This bullet refers to  Used for short term forecasting tracking these indicators to forecast future  It only focuses in primary goal changes.  These models focus only on the history of  Early information while waiting for the time series itself without considering actual estimate other related factors. -need to make decisions before you have the final data. Using early data to make Common Time Series Models/Procedures informed guesses about what the final Classical Methods numbers will be.  Decision making instrument in  These are traditional techniques used to preparation for future analyze and forecast time series data. They  involve breaking down the time series into  breaks down a time series into its component different components to better understand parts: trend, seasonality, and irregularity. and predict the data. This helps you understand what's driving changes in the data and allows for better Smoothing the Time series forecasting.  is a technique used to remove random Modern Methods fluctuations from the data to see the underlying trend more clearly.  use statistical models to describe and Decomposition forecast the behavior of the variable of interest (these provide optimal forecasts)  Decomposition means breaking down the time series into its different components to ARIMA Models understand the various influences on the data. There are typically four components:  Combines autoregression (using past values) and moving averages for better forecasting.  Trend: The general direction in which the  ARIMA models are advanced methods that data is moving over time (e.g., sales combine past data points (autoregression) increasing over several years). and past prediction errors (moving average)  Seasonal: Regular patterns that repeat over to make better forecasts. It’s like learning a specific period, like monthly or yearly from past mistakes and successes to predict (e.g., higher ice cream sales in summer). the future more accurately.  Business Cycle: Longer-term economic cycles that affect the data, like recessions or Volatility Models (ARCH, GARCH) booms.  Irregular Components: Random variations  These models are used when the variability or noise that can't be explained by the other of the data (how much it swings up and components. down) changes over time. The Use of Growth Rate in Forecasting Transfer Function Models  This involves looking at how fast something  Input, Process, Output Process is growing over time and using that  This model is used to understand the information to predict future values. relationship between input and output  Increasing over time variables. Trend Models Vector Autoregression  Identify and predict the overall direction  A model that predicts multiple related time (upward or downward) in the data over time. series variables simultaneously.  These models focus on identifying the long-  VAR models handle multiple time series term direction in which the data is moving. variables that might influence each other.  VAR model would analyze how these Moving Average variables interact and affect each other over time.  smooths out short-term fluctuations by averaging the data points within a certain Long Memory Models (Wavelets) period. This makes it easier to spot trends or patterns over time.  Detects long-term dependencies in the data, useful for complex time series. Exponential Smoothing Procedures  These models detect and forecast long-term dependencies in the data, which means they  Similar to moving averages, but with a twist: can identify patterns that persist over a long more weight is given to the most recent data period. points, making the model more responsive to recent changes in the data. This is useful Overview of Time Series Characteristics when you believe recent data is more informative of future trends. Univariate Time Series Decomposition  Is a sequence of measuremnts of the same variable collected over time.   The measurements are made at regular time data that cannot be easily explained or intervals. predicted.  The focus is on understanding one variable  Easter Effect/Moving Holidays (𝑬𝒕 ) -These are irregular effects that occur Types of Models because holidays like Easter move on the calendar each year, creating fluctuations in 2 basic types of time domain models data that are hard to predict.  Trading Day Variation (𝑻𝑫𝒕 ) 1. ARIMA (Autoregressive Integrated -Variations can also occur because of Moving Average) Models differences in the number of trading days -These relate current data to past data and (e.g., fewer trading days in February errors in predictions to improve forecasts. compared to other months), causing 2. Ordinary Regression Models irregular fluctuations. -These use time indices as variables to  Extreme Values/Outliers (𝑬′𝒕 ) analyze and predict trends. -Sometimes, data points are abnormally high or low due to unusual events (like a natural Components of Time Series disaster or economic shock), which are considered outliers. 1. Trend (𝑻𝒕 ) 5. Long Run Cycle/ Cyclic (𝑪𝒕 )  Refers to the long-term tendency of the series to increase or decrease; this is  it occurs when the data exhibit rises and considered as the underlying growth falls that are not of a fixed frequency (upward trend) or decline (downward trend)  in time series, any periodic variation  reflects the general direction in which the may be described as a cycle data is moving over a long period. It shows  Cyclic components are similar to whether the data is generally increasing, seasonality but occur over a longer, decreasing, or staying the same. irregular period. Cycles represent rises and falls in the data that are not tied to a 2. Seasonality (𝑺𝒕 ) fixed calendar period.  this is a periodic pattern of fluctuations that Decomposition Models repeats from year to year.  Each observation period is called a season Additive Models and the length of seasonality or periodicity is the number of seasons in a year This approach assumes that the components (Trend,  Seasonality refers to regular and predictable Cycle, Seasonality, and Irregularity) are added patterns that repeat at specific intervals together to form the observed data. It's used when within a year or another period. These the impact of components is consistent over time. fluctuations are due to factors like weather, holidays, or cultural events.  Formula: Zt=Tt+Ct+St+It  Formula: Zt=Tt+Ct+St+Et+E’t+TDt+It 3. Outliers Multiplicative Models  In regression, far away from your line  In time series data, far away from your other This approach assumes that the components data. multiply together to form the observed data. It’s  are data points that differ significantly from used when the impact of components varies other observations. They are unusually high proportionally with the level of the data. or low compared to the rest of the data.  Formula: Zt=Tt×Ct×St×It 4. Irregularity (𝑰𝒕 )  Formula: Zt=Tt×Ct×St×Et×E’t×TDt×It  random fluctuations; the “left over”; the part that is not taken into account by the trend, the cycle and the seasonality  there’s no trend, seasonality, and it has more outliers  refers to random fluctuations in the data that do not follow any pattern of trend, seasonality, or cycles. It’s the “noise” in the