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ARIMA (Auto-Regressive Integrated Moving Average)

Posted on January 27, 2021February 13, 2021 by Dexlab

This is another blog added to the series of time series forecasting. In this particular blog I will be discussing about the basic concepts of ARIMA model.

So what is ARIMA?

ARIMA also known as Autoregressive Integrated Moving Average is a time series forecasting model that helps us predict the future values on the basis of the past values. This model predicts the future values on the basis of the data’s own lags and its lagged errors.

When a data does not reflect any seasonal changes and plus it does not have a pattern of random white noise or residual then an ARIMA model can be used for forecasting.

There are three parameters attributed to an ARIMA model p, q and d :-

p :- corresponds to the autoregressive part

q:- corresponds to the moving average part.

d:- corresponds to number of differencing required to make the data stationary.

In our previous blog we have already discussed in detail what is p and q but what we haven’t discussed is what is d and what is the meaning of differencing (a term missing in ARMA model).

Since AR is a linear regression model and works best when the independent variables are not correlated, differencing can be used to make the model stationary which is subtracting the previous value from the current value so that the prediction of any further values can be stabilized . In case the model is already stationary the value of d=0. Therefore “differencing is the minimum number of deductions required to make the model stationary”. The order of d depends on exactly when your model becomes stationary i.e. in case the autocorrelation is positive over 10 lags then we can do further differencing otherwise in case autocorrelation is very negative at the first lag then we have an over-differenced series.

The formula for the ARIMA model would be:-

To check if ARIMA model is suited for our dataset i.e. to check the stationary of the data we will apply Dickey Fuller test and depending on the results we will using differencing.

In my next blog I will be discussing about how to perform time series forecasting using ARIMA model manually and what is Dickey Fuller test and how to apply that, so just keep on following us for more.

So, with that we come to the end of the discussion on the ARIMA Model. Hopefully it helped you understand the topic, for more information you can also watch the video tutorial attached down this blog. The blog is designed and prepared by Niharika Rai, Analytics Consultant, DexLab Analytics DexLab Analytics offers machine learning courses in Gurgaon. To keep on learning more, follow DexLab Analytics blog.

Time Series Analysis & Modelling with Python (Part II) – Data Smoothing

Posted on January 20, 2021January 20, 2021 by Dexlab

Data Smoothing is done to better understand the hidden patterns in the data. In the non- stationary processes, it is very hard to forecast the data as the variance over a period of time changes, therefore data smoothing techniques are used to smooth out the irregular roughness to see a clearer signal.

In this segment we will be discussing two of the most important data smoothing techniques :-

Moving average smoothing
Exponential smoothing

Moving average smoothing

Moving average is a technique where subsets of original data are created and then average of each subset is taken to smooth out the data and find the value in between each subset which better helps to see the trend over a period of time.

Lets take an example to better understand the problem.

Suppose that we have a data of price observed over a period of time and it is a non-stationary data so that the tend is hard to recognize.

QTR (quarter)	Price
1	10
2	11
3	18
4	14
5	15
6	?

In the above data we don’t know the value of the 6^th quarter.

….fig (1)

The plot above shows that there is no trend the data is following so to better understand the pattern we calculate the moving average over three quarter at a time so that we get in between values as well as we get the missing value of the 6^th quarter.

To find the missing value of 6^th quarter we will use previous three quarter’s data i.e.

MAS = = 15.7

QTR (quarter)	Price
1	10
2	11
3	18
4	14
5	15
6	15.7

MAS = = 13

MAS = = 14.33

QTR (quarter)	Price	MAS (Price)
1	10	10
2	11	11
3	18	18
4	14	13
5	15	14.33
6	15.7	15.7

….. fig (2)

In the above graph we can see that after 3^rd quarter there is an upward sloping trend in the data.

Exponential Data Smoothing

In this method a larger weight ( ) which lies between 0 & 1 is given to the most recent observations and as the observation grows more distant the weight decreases exponentially.

The weights are decided on the basis how the data is, in case the data has low movement then we will choose the value of closer to 0 and in case the data has a lot more randomness then in that case we would like to choose the value of closer to 1.

EMA= F_t= F_t-1 + (A_t-1 – F_t-1)

Now lets see a practical example.

For this example we will be taking = 0.5

Taking the same data……

QTR (quarter)	Price (A_t)	EMS Price(F_t)
1	10	10
2	11	?
3	18	?
4	14	?
5	15	?
6	?	?

To find the value of yellow cell we need to find out the value of all the blue cells and since we do not have the initial value of F₁ we will use the value of A_1.Now lets do the calculation:-

F₂=10+0.5(10 – 10) = 10

F₃=10+0.5(11 – 10) = 10.5

F₄=10.5+0.5(18 – 10.5) = 14.25

F₅=14.25+0.5(14 – 14.25) = 14.13

F₆=14.13+0.5(15 – 14.13)= 14.56

QTR (quarter)	Price (A_t)	EMS Price(F_t)
1	10	10
2	11	10
3	18	10.5
4	14	14.25
5	15	14.13
6	14.56	14.56

In the above graph we see that there is a trend now where the data is moving in the upward direction.

So, with that we come to the end of the discussion on the Data smoothing method. Hopefully it helped you understand the topic, for more information you can also watch the video tutorial attached down this blog. The blog is designed and prepared by Niharika Rai, Analytics Consultant, DexLab Analytics DexLab Analytics offers machine learning courses in Gurgaon. To keep on learning more, follow DexLab Analytics blog.

Time Series Analysis Part I

Posted on January 18, 2021January 18, 2021 by Dexlab

A time series is a sequence of numerical data in which each item is associated with a particular instant in time. Many sets of data appear as time series: a monthly sequence of the quantity of goods shipped from a factory, a weekly series of the number of road accidents, daily rainfall amounts, hourly observations made on the yield of a chemical process, and so on. Examples of time series abound in such fields as economics, business, engineering, the natural sciences (especially geophysics and meteorology), and the social sciences.

Univariate time series analysis- When we have a single sequence of data observed over time then it is called univariate time series analysis.
Multivariate time series analysis – When we have several sets of data for the same sequence of time periods to observe then it is called multivariate time series analysis.

The data used in time series analysis is a random variable (Yt) where t is denoted as time and such a collection of random variables ordered in time is called random or stochastic process.

Stationary: A time series is said to be stationary when all the moments of its probability distribution i.e. mean, variance , covariance etc. are invariant over time. It becomes quite easy forecast data in this kind of situation as the hidden patterns are recognizable which make predictions easy.

Non-stationary: A non-stationary time series will have a time varying mean or time varying variance or both, which makes it impossible to generalize the time series over other time periods.

Non stationary processes can further be explained with the help of a term called Random walk models. This term or theory usually is used in stock market which assumes that stock prices are independent of each other over time. Now there are two types of random walks:
Random walk with drift : When the observation that is to be predicted at a time ‘t’ is equal to last period’s value plus a constant or a drift (α) and the residual term (ε). It can be written as
Yt= α + Yt-1 + εt
The equation shows that Yt drifts upwards or downwards depending upon α being positive or negative and the mean and the variance also increases over time.
Random walk without drift: The random walk without a drift model observes that the values to be predicted at time ‘t’ is equal to last past period’s value plus a random shock.
Yt= Yt-1 + εt
Consider that the effect in one unit shock then the process started at some time 0 with a value of Y0
When t=1
Y1= Y0 + ε1
When t=2
Y2= Y1+ ε2= Y0 + ε1+ ε2
In general,
Yt= Y0+∑ εt
In this case as t increases the variance increases indefinitely whereas the mean value of Y is equal to its initial or starting value. Therefore the random walk model without drift is a non-stationary process.

So, with that we come to the end of the discussion on the Time Series. Hopefully it helped you understand time Series, for more information you can also watch the video tutorial attached down this blog. DexLab Analytics offers machine learning courses in delhi. To keep on learning more, follow DexLab Analytics blog.

Here’s All You Need to Know about DexLab Analytics’ Market Risk Modelling Live Demo Session

Posted on October 16, 2017October 24, 2017 by Dexlab

DexLab Analytics brings Market Risk Modelling training to India. Internet has helped people become technology-driven. Digital transformation is evident all around us. No more, gaining knowledge is a task like moving mountains – right from the confinements of your home, you can now get access to a plethora of information and knowledge, thanks to online learning. Several professionals and students are opting for e-learning method of education, owing to its flexibility and ease of access. And India is not lagging behind in this. Several online classes and sessions are being organized by premier data science learning institutes in India, and DexLab Analytics is one of them.

DexLab Analytics is here with an intensive live demo session on Market Risk Modelling Online for free. The online workshop is taking place on 25^th October, 2017 from 10:00PM IST onwards, and will solely focus on how Market Risk Analytics has grown to be the new in-demand analytics course for the financial sector. Our in-house trainers will extensively explain the nitty-gritty of MRM, including its importance, major components, and why is it a must-to-have skill for the future. The interested candidates are asked to register as soon as possible by penning down a mail to DexLab Analytics, mentioning they would attend the workshop on the specified date and time.

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