A Moving Average is a process where each value is a function of the noise in the past observations. These are the random error terms which follow a white noise process. The general form is MA(q), where xt depends on q past values. Just like AR models, this also has a regression like structure, however, instead […]

## Forecasting with AutoRegressive (AR) Model in R

Now that we know how to estimate the AR model using ARIMA, we can create a simple forecast based on the model. Step 1: Fit the model The first step is to fit the model as ARIMA(1, 0, 0). We have already seen this in the previous lesson.

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> msft_ar<-arima(msft_ts,c(1,0,0)) |

Step 2: Create Forecast We can now […]

## Estimating AutoRegressive (AR) Model in R

We will now see how we can fit an AR model to a given time series using the arima() function in R. Recall that AR model is an ARIMA(1, 0, 0) model. We can use the arima() function in R to fit the AR model by specifying the order = c(1, 0, 0). We will perform the estimation using the msft_ts time series that […]

## AutoRegressive (AR) Model in R

AutoRegressive (AR) model is one of the most popular time series model. In this model, each value is regressed to its previous observations. AR(1) is the first order autoregression meaning that the current value is based on the immediately preceding value. We can use the arima.sim() function to simulate the AutoRegressive (AR) model. Note that model argument […]

## Simulate Random Walk (RW) in R

When a series follows a random walk model, it is said to be non-stationary. We can stationarize it by taking a first-order difference of the time series, which will produce a stationary series, that is, a Zero Mean White Noise series. For example, the stock prices of a stock follow a random walk model, and […]

## Simulate White Noise (WN) in R

The function arima.sim() can be used to simulate data from a variety of time series models. Based on the model we want to apply, we specify the appropriate values for p, d and q to the model ARIMA(p,d,q). The general format for the arima.sim() function is as follows: For the White Noise model, all p, d and q in arima […]

## ARIMA Modeling

If we combine differencing with autoregression and a moving average model, we obtain a non-seasonal ARIMA model. ARIMA is an acronym for AutoRegressive Integrated Moving Average model. The term “integration” in this context is the reverse of differencing. ARIMA model is represented as ARIMA(p,d,q) Where: p = order of the autoregressive part d = degree of first differencing […]

## Time Series Models

By now we have a strong foundational understanding of various concepts essential for time series analysis. The rest of the course will focus on the following: A theoretical understanding of the important time series models (White Noise, AutoRegressive (AR), Moving Average (MA), ARMA. The ARIMA model and how various time series processes can be explained […]

## Autocorrelation in R

Autocorrelation is an important part of time series analysis. It helps us understand how each observation in a time series is related to its recent past observations. When autocorrelation is high in a time series, it becomes easy to predict their future observations. Let us consider the Microsoft stock prices for the year 2016, which […]

## Differencing and Log Transformation

Removing Variability Using Logarithmic Transformation Since the data shows changing variance over time, the first thing we will do is stabilize the variance by applying log transformation using the log() function. The resulting series will be a linear time series. Removing Linear Trend We will now perform the first difference transformation [z(t) – z(t-1)] to our series to remove […]