In data science, we often times need to do the analysis of events based on some time. This analysis can help us analyse the previous trends and predict future trends of events. And thus, time series forecasting came into the picture. Time series forecasting methods help us to predict events through a sequence of time.
In this blog, we will discuss the time series forecasting methods in detail. So without any further wait, let’s start learning!
Time Series Forecasting
Time series forecasting is a technique used to predict future values based on historical trends. It uses sequential data with an assumption that the future trend will be similar to the historical trend. It is also widely used in machine learning as a supervised learning problem. We can apply various ML algorithms to increase its accuracy, such as Regression, Random Forest, XGBoost, etc.
One example of time series forecasting is the prediction of stock market prices. For this, the historical data of a company's stock prices are considered the main dataset. After that, various time series forecasting methods are used as ML models, which are trained on this dataset. After training and evaluating the models, the final prediction is made based on the outcomes of those models.
Characteristics of Time Series Data
Before learning about methods of time series forecasting, we should be familiar with time series data itself. Below are some characteristics of time series data.
Time Dependence: As time series data is collected over a period of time, it is highly dependent on time. The order of data points decides the specific time period associated with that point.
Trend: Trends are the long-term changes or pattern which occurs in the data over time. A trend can be increasing, decreasing, or stationary.
Seasonality: It is an important character of time series data. Seasonality refers to the repeating fluctuations or patterns in the data that occur at a regular interval of time. This interval can occur annually, monthly, quarterly, etc.
Random Error: The random error is the noise present in the data. This noise affects the accuracy of the prediction, and thus it should be lowered as possible.
Autocorrelation: It is a key characteristic of time series data. In autocorrelated data, the past values of data are correlated with present values.
Types of Forecasting Methods
There are several types of forecasting methods to make predictions. Below are the most used forecasting methods.
Moving Average Model
Exponential Smoothing Model
Autoregressive Model
Autoregressive Moving Average Model (ARMA)
Autoregressive Integrated Moving Average Model (ARIMA)
Moving Average Model
Moving average is the most widely used time series forecasting technique. It smoothens out the fluctuations in data in order to identify new trends. It is a very simple and intuitive method. It is very handy in short-term predictions to smoothen out random noises in the data. In this model, we calculate the average of a certain number of periods up to that point in time.
The moving average is typed as follows:
Simple Moving Average
Weighted Moving Average
Formula
The formula for calculating the simple moving average is:
Here, n represents the total number of observations, and Xi represents the data point at the ith period.
The formula for calculating the weighted moving average is:
Here, Xi is the data point at a given period with Wi weightage.
Advantages
Below are a few pros of the moving average model in time series forecasting.
It is highly simple to implement and understand.
It quickly adjusts to changes in data.
It makes reliable predictions with limited data.
Disadvantages
Below are a few cons of the moving average model in time series forecasting.
This model is not useful for long-term predictions.
It can cause over smoothening of data and thus can cause loss of important patterns.
It is not suitable for non-stationary data.
Exponential Smoothing Model
Exponential smoothing is another time series forecasting method. In this method, we combine the most recent and previous forecasted values. With each addition, the forecast is updated, and thus, the weight of the last estimates drops exponentially. This method is highly effective when the time series parameters vary slowly over time.
This method is used with simple univariate data with no seasonal and trend patterns. It requires a single parameter called the smoothing factor (α). This parameter is set between 0 and 1, and it controls the rate of drop in past observations.
Formula
The formula for simple exponential smoothing is given as follows:
Description
S(t+1): It is the forecast for the next period.
α: It is the smoothing constant.
Yt: It is the observed value of series in period ‘t’.
St: It is the old forecast for the period ‘t’.
Advantages
A few pros of exponential smoothing are given below.
It is more flexible and provides accurate results.
It can handle time series data with or without trends as well as seasonality.
It gives more significance to recent observations.
Disadvantages
A few pros of exponential smoothing are given below.
It relies heavily on historical data, and thus it can produce incorrect results when historical data is limited.
It cannot capture patterns with cyclic nature or odd seasonality.
The selection of proper smoothing parameters is very complex and time taking.
Autoregressive Model
The autoregressive (AR) model is another time series forecasting method that forecasts future trends based on past trends of data. It is used when there is a correlation between the time series values and their preceding and succeeding values. It is based on the assumption that the values of time series are linearly dependent on their previous values.
In the autoregressive model, the forecast value at a given time is a linear combination of past p observations. Here, p is also called the order of the autoregressive model.
Formula
The formula for the AR model is as follows:
Description
Xt: It is the forecast value at time ‘t’.
X(t-1): It is the observed value at time ‘t-1’.
C: It is the constant or intercept value.
Et: It is the error term at time ‘t’.
Advantages
Some perks of the autoregressive model are:
It is the building block for the ARIMA model.
It can be used for real-time forecasting tasks.
It works well with stationary time series data.
Disadvantages
Some drawbacks of the autoregressive model are:
The accuracy of the AR model can reduce if there is less historical time series data.
This model may not work well for non-linear data.
It is very sensitive to outliers in data and can produce inaccurate results.
Autoregressive Moving Average Model
The name ARMA is commonly used for autoregressive moving average models. The name ARMA is derived from the autoregressive (AR) and moving average (MA) models. It is used when data exhibits both autocorrelation and moving average nature. However, it may not capture advanced patterns, and thus, a more advanced model like ARIMA is considered.
Formula
The formula for the ARMA model is as follows:
Description
Yt: It is the observed value at time ‘t’.
c: It is the intercept or constant term.
Φi: It is the autoregressive coefficient.
Y(t-i): It represents the observed value at the time (t-i).
εt: It is the error term at time ‘t’.
ε(t-i): It is the forecast error at the time (t-i).
Advantages
Some pros of the ARMA model are as follows:
There is no assumption needed for seasonability in data.
It is a very robust model, and it can handle large noises and irregularities in the data.
It can be extended to higher levels easily.
Disadvantages
Some cons of the ARMA model are as follows:
It is difficult to choose the optimal order of the ARMA model.
It assumes stationarity in the data. Thus it may not hold in many complex time series.
It is sensitive to outliers in the data.
Autoregressive Integrated Moving Average Model
The name ARIMA is generally used for autoregressive integrated moving average models. This model combines autoregressive (AR), differencing (I), and moving average (MA) models. Here, the differencing is used to remove the trends and seasonality from the given data. This model can handle non-stationary data and capture both moving average and autoregressive patterns.
Formula
The formula for the ARIMA model is as follows:
Description
Yt: It is the observed value at time ‘t’.
Bi: It is the autoregressive coefficient.
Y(t-i): It represents the observed value at the time (t-i).
εt: It is the error term at time ‘t’.
ε(t-q): It is the forecast error at the time (t-q).
Advantages
Now let’s look at a few benefits of the ARIMA model.
It can convert non-stationary data into stationary data.
It uses efficient algorithms to estimate parameters for the equation.
It can also provide reliable forecasts and confidence intervals, as it is based on statistical methods and theory.
Disadvantages
Even though the mode has a lot of pros but there are a few cons as well, which are as follows.
It is not suitable for multivariate time series data.
For large data values, the computation of the ARIMA model becomes quite complex.
Due to its complex nature, there is a possibility of overfitting of data.
Frequently Asked Questions
What is time series data?
Time series data is the sequence of data recorded at various intervals of time in a specific order.
What is time series forecasting?
Time series forecasting is a technique which is used to predict future patterns based on past patterns.
What is the limitation of time series forecasting methods?
Time series forecasting methods may not work well when the data has irregular patterns and can be affected by external factors.
Which libraries are used in time series forecasting?
The Numpy library in Python and forecast and time series packages in R are used in time series forecasting.
Conclusion
This article discusses the time series forecasting methods. We discussed time series data and various methods for its forecasting in detail. We hope this blog has helped you enhance your knowledge of time series forecasting. If you want to learn more, then check out our articles.
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