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Time Series Analysis Part I


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.


AI-Related Tech Jargons You Need To Learn Right Now

AI-Related Tech Jargons You Need To Learn Right Now

As artificial intelligence gains momentum and becomes more intricate in nature, technological jargons may turn unfamiliar to you. Evolving technologies give birth to a smorgasbord of new terminologies. In this article, we have tried to compile a few of such important terms that are related to AI. Learn, assimilate and flaunt them in your next meeting.

Artificial Neuron Networks – Not just an algorithm, Artificial Neuron Networks is a framework containing different machine learning algorithms that work together and analyzes complex data inputs.

Backpropagation – It refers to a process in artificial neural networks used to discipline deep neural networks. It is widely used to calculate a gradient that is required in calculating weights found across the network.


Bayesian Programming – Revolving around the Bayes’ Theorem, Bayesian Programming declares the probability of something happening in the future based on past conditions relating to the event.

Analogical Reasoning – Generally, the term analogical indicates non-digital data but when in terms of AI, Analogical Reasoning is the method of drawing conclusions studying the past outcomes. It’s quite similar to stock markets.

Data Mining – It refers to the process of identifying patterns from fairly large data sets with the help statistics, machine learning and database systems in combination.

Decision Tree LearningUsing a decision tree, you can move seamlessly from observing an item to drawing conclusions about the item’s target value. The decision tree is represented as a predictive model, the observation as the branches and the conclusion as the leaves.

Behavior Informatics (BI) – It is of extreme importance as it helps obtain behavior intelligence and insights.

Case-based Reasoning (CBR) – Generally speaking, it defines the process of solving newer challenges based on solutions that worked for similar past issues.

Feature Extraction – In machine learning, image processing and pattern recognition plays a dominant role. Feature Extraction begins from a preliminary set of measured data and ends up building derived values that intend to be non-redundant and informative – leading to improved subsequent learning and even better human interpretations.

Forward Chaining – Also known as forward reasoning, Forward Chaining is one of two main methods of reasoning while leveraging an inference engine. It is a widely popular implementation strategy best suited for business and production rule systems. Backward Chaining is the exact opposite of Forwarding Chaining.

Genetic Algorithm (GA) – Inspired by the method of natural selection, Genetic Algorithm (GA) is mainly used to devise advanced solutions to optimization and search challenges. It works by depending on bio-inspired operators like crossover, mutation and selection.

Pattern Recognition – Largely dependent on machine learning and artificial intelligence, Pattern Recognition also involves applications, such as Knowledge Discovery in Databases (KDD) and Data Mining.

Reinforcement Learning (RL) – Next to Supervised Learning and Unsupervised Learning, Reinforcement Learning is another machine learning paradigms. It’s reckoned as a subset of ML that deals with how software experts should take actions in circumstances so as to maximize notions of cumulative reward.

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