2020. 1. 24. 05:03ㆍ카테고리 없음
Moving Average Smoothing for Data Preparation, Feature Engineering, and Time Series Forecasting with PythonPhoto by, some rights reserved. Moving Average SmoothingSmoothing is a technique applied to time series to remove the fine-grained variation between time steps.The hope of smoothing is to remove noise and better expose the signal of the underlying causal processes. Moving averages are a simple and common type of smoothing used in time series analysis and time series forecasting.Calculating a moving average involves creating a new series where the values are comprised of the average of raw observations in the original time series.A moving average requires that you specify a window size called the window width. This defines the number of raw observations used to calculate the moving average value.The “moving” part in the moving average refers to the fact that the window defined by the window width is slid along the time series to calculate the average values in the new series.There are two main types of moving average that are used: Centered and Trailing Moving Average. Centered Moving AverageThe value at time (t) is calculated as the average of raw observations at, before, and after time (t).For example, a center moving average with a window of 3 would be calculated as. Centerma(t) = mean(obs(t-1), obs(t), obs(t+1))This method requires knowledge of future values, and as such is used on time series analysis to better understand the dataset.A center moving average can be used as a general method to remove trend and seasonal components from a time series, a method that we often cannot use when forecasting.
Trailing Moving AverageThe value at time (t) is calculated as the average of the raw observations at and before the time (t).For example, a trailing moving average with a window of 3 would be calculated as. Trailma(t) = mean(obs(t-2), obs(t-1), obs(t))Trailing moving average only uses historical observations and is used on time series forecasting.It is the type of moving average that we will focus on in this tutorial. Data ExpectationsCalculating a moving average of a time series makes some assumptions about your data.It is assumed that both trend and seasonal components have been removed from your time series.This means that your time series is stationary, or does not show obvious trends (long-term increasing or decreasing movement) or seasonality (consistent periodic structure).There are many methods to remove trends and seasonality from a time series dataset when forecasting. Two good methods for each are to use the differencing method and to model the behavior and explicitly subtract it from the series.Moving average values can be used in a number of ways when using machine learning algorithms on time series problems.In this tutorial, we will look at how we can calculate trailing moving average values for use as data preparation, feature engineering, and for directly making predictions.Before we dive into these examples, let’s look at the Daily Female Births dataset that we will use in each example.
Smoothed Moving Average Formula
Daily Female Births Dataset Plot Moving Average as Data PreparationMoving average can be used as a data preparation technique to create a smoothed version of the original dataset.Smoothing is useful as a data preparation technique as it can reduce the random variation in the observations and better expose the structure of the underlying causal processes.The function on the Series Pandas object will automatically group observations into a window. You can specify the window size, and by default a trailing window is created.
Smoothed Moving Average Formula
MACD is, by definition calculated as a difference of fast and slow EMA (Exponential Moving Average). This versions allows you to: use one of the 4 basic types of averages for calculation: simple moving average; exponential moving average; smoothed moving average; linear weighted moving average; it is normalizing those macd values to -1 to +1 range.
Once the window is created, we can take the mean value, and this is our transformed dataset.New observations in the future can be just as easily transformed by keeping the raw values for the last few observations and updating a new average value.To make this concrete, with a window size of 3, the transformed value at time (t) is calculated as the mean value for the previous 3 observations (t-2, t-1, t), as follows. Zoomed Moving Average TransformHere, you can clearly see the lag in the transformed dataset.Next, let’s take a look at using the moving average as a feature engineering method.
Moving Average as Feature EngineeringThe moving average can be used as a source of new information when modeling a time series forecast as a supervised learning problem.In this case, the moving average is calculated and added as a new input feature used to predict the next time step.First, a copy of the series must be shifted forward by one time step. This will represent the input to our prediction problem, or a lag=1 version of the series. This is a standard supervised learning view of the time series problem. Obs2,obs3Next, a second copy of the series needs to be shifted forward by one, minus the window size. This is to ensure that the moving average summarizes the last few values and does not include the value to be predicted in the average, which would be an invalid framing of the problem as the input would contain knowledge of the future being predicted.For example, with a window size of 3, we must shift the series forward by 2 time steps.
This is because we want to include the previous two observations as well as the current observation in the moving average in order to predict the next value. We can then calculate the moving average from this shifted series.Below is an example of how the first 5 moving average values are calculated. Remember, the dataset is shifted forward 2 time steps and as we move along the time series, it takes at least 3 time steps before we even have enough data to calculate a window=3 moving average.
9 39.000000 38.0 27The next section will look at how to use the moving average as a naive model to make predictions. Moving Average as PredictionThe moving average value can also be used directly to make predictions.It is a naive model and assumes that the trend and seasonality components of the time series have already been removed or adjusted for.The moving average model for predictions can easily be used in a walk-forward manner. As new observations are made available (e.g. Daily), the model can be updated and a prediction made for the next day.We can implement this manually in Python.
Below is an example of the moving average model used in a walk-forward manner. Hello,thank you for all the articles and books, they are great.Here I am not sure about one thing. Is the shift(width - 1) correct?
In this code:width = 3lag1 = df.shift(1)lag3 = df.shift(width – 1)I think it should be always shift(2), no matter what is the width, because we do the shift to skip only one single current value (so it is not included in the window later).For example for an input series df=1,2,3,4,5,6,7 and width=4 there will be shift(3) that leads to:t t+1 shift(3) mean– 1 – –1 2 – –2 3 – –3 4 1 –4 5 2 –5 6 3 –6 7 4 2,5but the mean 2,5 belongs to t=5, not t=6, right?But of course maybe I just didn’t understand it correctly. Speaking of shifting-time, I think you can help my current work about forecasting time series with Generalized Linear Model. The reason why I use GLM method is I consider temperature (T(t),T(t-1),), rainfall (R(t),R(t-1),), humidity (H(t),H(t-1),), and past event (Y(t-1),) as the explanatory variables to current event (Y(t)). Let’s say Y(t)T(t)+R(t)+H(t)+Y(t-1)+T(t-1)+R(t-1)+H(t-1) for lag-1. By comparing plots, I can see that my prediction at time t consistently more looks alike the real obervation at time t-1. I say it’s like shifting (delay) one time-step.
I have no idea why this is happening. I think it’s related to “time series” as random walk process. Can you explain me why? Thank you in advance, Jason. I’m a student by the way, so I do really appreciate your help.