NEW COURSE: Time Series Analysis, Forecasting, and Machine Learning in Python

June 16, 2021

Time Series Analysis, Forecasting, and Machine Learning in Python

VIP Promotion

The complete Time Series Analysis course has arrived

Hello friends!

2 years ago, I asked the students in my Tensorflow 2.0 course if they’d be interested in a course on time series. The answer was a resounding YES.

Don’t want to read the rest of this little spiel? Just get the coupon:

https://www.udemy.com/course/time-series-analysis/?couponCode=TIMEVIP

(Updated: Expires Aug 17, 2021) https://www.udemy.com/course/time-series-analysis/?couponCode=TIMEVIP2

(note: this VIP coupon expires in 30 days!)

Time series analysis is becoming an increasingly important analytical tool.

  • With inflation on the rise, many are turning to the stock market and cryptocurrencies in order to ensure their savings do not lose their value.
  • COVID-19 has shown us how forecasting is an essential tool for driving public health decisions.
  • Businesses are becoming increasingly efficient, forecasting inventory and operational needs ahead of time.

Let me cut to the chase. This is not your average Time Series Analysis course. This course covers modern developments such as deep learning, time series classification (which can drive user insights from smartphone data, or read your thoughts from electrical activity in the brain), and more.

We will cover techniques such as:

  • ETS and Exponential Smoothing
  • Holt’s Linear Trend Model
  • Holt-Winters Model
  • ARIMA, SARIMA, SARIMAX, and Auto ARIMA
  • ACF and PACF
  • Vector Autoregression and Moving Average Models (VAR, VMA, VARMA)
  • Machine Learning Models (including Logistic Regression, Support Vector Machines, and Random Forests)
  • Deep Learning Models (Artificial Neural Networks, Convolutional Neural Networks, and Recurrent Neural Networks)
  • GRUs and LSTMs for Time Series Forecasting

We will cover applications such as:

  • Time series forecasting of sales data
  • Time series forecasting of stock prices and stock returns
  • Time series classification of smartphone data to predict user behavior

The VIP version of the course (obtained by purchasing the course NOW during the VIP period) will cover even more exciting topics, such as:

  • AWS Forecast (Amazon’s state-of-the-art low-code forecasting API)
  • GARCH (financial volatility modeling)
  • FB Prophet (Facebook’s time series library)
  • And MORE (it’s a secret!)

As always, please note that the VIP period may not last forever, and if / when the course becomes “non-VIP”, the VIP contents will be removed. If you purchased the VIP version, you will retain permanent access to the VIP content via my website, simply by letting me know via email you’d like access (you only need to email if I announce the VIP period is ending).

Small note:

I wanted to get this course into your hands early. Some sections are still in the editing stages, particularly:

  • Convolutional Neural Networks (done, but more to be added later)
  • Recurrent Neural Networks (done, but more to be added later)
  • Vector Autoregression
  • (VIP) GARCH
  • (VIP) FB Prophet
  • +MORE VIP CONTENT (it’s a surprise!)

UPDATE: The crossed-out items have since been added. There is no timeline for the remaining “surprise” lectures – it’ll be a surprise! 😉

So what are you waiting for? Get the VIP version of Time Series Analysis NOW:

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NEW COURSE: Financial Engineering and Artificial Intelligence in Python

September 8, 2020

Financial Engineering and Artificial Intelligence in Python

VIP Promotion

The complete Financial Engineering course has arrived

Hello once again friends!

Today, I am announcing the VIP version of my latest course: Financial Engineering and Artificial Intelligence in Python.

If you don’t want to read my little spiel just click here to get your VIP coupon:

https://www.udemy.com/course/ai-finance/?couponCode=FINANCEVIP (expires Oct 9, 2020)

https://www.udemy.com/course/ai-finance/?couponCode=FINANCEVIP11 (expires Aug 17, 2021)

(as usual, this coupon lasts only 30 days, so don’t wait!)

This is a MASSIVE (20 hours) Financial Engineering course covering the core fundamentals of financial engineering and financial analysis from scratch. We will go in-depth into all the classic topics, such as:

  • Exploratory data analysis, significance testing, correlations
  • Alpha and beta
  • Advanced Pandas Data Frame manipulation for time series and finance
  • Time series analysis, simple moving average, exponentially-weighted moving average
  • Holt-Winters exponential smoothing model
  • ARIMA and SARIMA
  • Efficient Market Hypothesis
  • Random Walk Hypothesis
  • Time series forecasting (“stock price prediction”)
  • Modern portfolio theory
  • Efficient frontier / Markowitz bullet
  • Mean-variance optimization
  • Maximizing the Sharpe ratio
  • Convex optimization with Linear Programming and Quadratic Programming
  • Capital Asset Pricing Model (CAPM)
  • Algorithmic trading

In addition, we will look at various non-traditional techniques which stem purely from the field of machine learning and artificial intelligence, such as:

  • Regression models
  • Classification models
  • Unsupervised learning
  • Reinforcement learning and Q-learning

We will learn about the greatest flub made in the past decade by marketers posing as “machine learning experts” who promise to teach unsuspecting students how to “predict stock prices with LSTMs”. You will learn exactly why their methodology is fundamentally flawed and why their results are complete nonsense. It is a lesson in how not to apply AI in finance.

List of VIP-only Contents

As with my Tensorflow 2 release, some of the VIP content will be a surprise and will be released in stages. Currently, the entirety of the Algorithmic Trading sections are VIP sections. Newly added VIP sections include Statistical Factor Models and “The Lazy Programmer Bonus Offer”. Here’s a full list:

Classic Algorithmic Trading – Trend Following Strategy

You will learn how moving averages can be applied to do algorithmic trading.

Machine Learning-Based Trading Strategy

Forecast returns in order to determine when to buy and sell.

Reinforcement Learning-Based (Q-Learning) Trading Strategy

I give you a full introduction to Reinforcement Learning from scratch, and then we apply it to build a Q-Learning trader. Note that this is *not* the same as the example I used in my Tensorflow 2, PyTorch, and Reinforcement Learning courses. I think the example included in this course is much more principled and robust.

Statistical Factor Models

The CAPM is one of the most renowned financial models in history, but did you know it’s only the simplest factor model, with just a single factor? To go beyond just this single factor model, we will learn about statistical factor models, where the multiple “factors” are found automatically using only the data.

The Lazy Programmer Bonus Offer

There are marketers out there who want to capitalize on your enthusiastic interest in finance, and unfortunately what they are teaching you is utter and complete garbage.

They will claim that they can “predict stock prices with LSTMs” and show you charts like this with nearly perfect stock price predictions.

Hint: if they can do this, why do they bother putting effort into making courses? Wouldn’t they already be billionaires?

Have you ever wondered if you are taking such a course from a fake data scientist / marketer? If so, just send me a message, and I will tell you whether or not you are taking such a course. (Hint: many of you are) I will give you a list of mistakes they made so you can look out for them yourself, and avoid “learning” things which will ultimately make YOU look very bad in front of potential future employers.

Believe me, if you ever try to get a job in machine learning or data science and you talk about a project where you “predicted stock prices with LSTMs”, all you will be demonstrating is how incompetent you are.

Save yourself from this embarrassing scenario by taking the “Lazy Programmer Offer”!

Please note: The VIP coupon will work only for the next month (starting from the coupon creation time). It’s unknown whether the VIP period will renew after that time.

After that, although the VIP content will be removed from Udemy, all who purchased the VIP course will get permanent free access to these VIP contents on deeplearningcourses.com.

In case it’s not clear, the process is very easy. For those folks who need the “step-by-step” instructions…:

STEP 1) I announce the VIP content will be removed.

STEP 2) You email me with proof that you purchased the course during the VIP period. Do NOT email me earlier as it will just get buried.

STEP 3) I will give you free access to the VIP materials for this course on deeplearningcourses.com.

Benefits of taking this course

  • Learn the knowledge you need to work at top tier investment firms
  • Gain practical, real-world quantitative skills that can be applied within and outside of finance
  • Make better decisions regarding your own finances

Personally, I think this is the most interesting and action-packed course I have created yet. My last few courses were cool, but they were all about topics which I had already covered in the past! GANs, NLP, Transfer Learning, Recommender Systems, etc etc. all just machine learning topics I have covered several times in different libraries. This course contains new, fresh content and concepts I have never covered in any of my courses, ever.

This is the first course I’ve created that extends into a niche area of AI application. It goes outside of AI and into domain expertise. An in-depth topic such as finance deserves its own course. This is that course. These are topics you will never learn in a generic data science or machine learning course. However, as a student of AI, you will recognize many of our tools and methods being applied, such as statistical inference, supervised and unsupervised learning, convex optimization, and optimal control. This allows us to go deeper than your run of the mill financial engineering course, and it becomes more than just the sum of its parts.

So what are you waiting for?

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The complete PyTorch course for AI and Deep Learning has arrived

April 1, 2020

PyTorch: Deep Learning and Artificial Intelligence

VIP Promotion

The complete PyTorch course has arrived

Hello friends!

I hope you are all staying safe. Well, I’m sure you’ve heard enough about that so how about some different news?

Today, I am announcing the VIP version of my latest course: PyTorch: Deep Learning and Artificial Intelligence

[If you don’t want to read my little spiel just click here to get your VIP coupon: https://www.udemy.com/course/pytorch-deep-learning/?couponCode=PYTORCHVIP]

https://www.udemy.com/course/pytorch-deep-learning/?couponCode=PYTORCHVIP16 (expires Aug 17, 2021)

This is a MASSIVE (over 22 hours) Deep Learning course covering EVERYTHING from scratch. That includes:

  • Machine learning basics (linear neurons)
  • ANNs, CNNs, and RNNs for images and sequence data
  • Time series forecasting and stock predictions (+ why all those fake data scientists are doing it wrong)
  • NLP (natural language processing)
  • Recommender systems
  • Transfer learning for computer vision
  • GANs (generative adversarial networks)
  • Deep reinforcement learning and applying it by building a stock trading bot

IN ADDITION, you will get some unique and never-before-seen VIP projects:

Estimating prediction uncertainty

Drawing the standard deviation of the prediction along with the prediction itself. This is useful for heteroskedastic data (that means the variance changes as a function of the input). The most popular application where heteroskedasticity appears is stock prices and stock returns – which I know a lot of you are interested in.

It allows you to draw your model predictions like this:


Sometimes, the data is simply such that a spot-on prediction can’t be made. But we can do better by letting the model tell us how certain it is in its predictions.

Facial recognition with siamese networks

This one is cool. I mean, I don’t have to tell you how big facial recognition has become, right? It’s the single most controversial technology to come out of deep learning. In the past, we looked at simple ways of doing this with classification, but in this section I will teach you about an architecture built specifically for facial recognition.

You will learn how this can work even on small datasets – so you can build a network that recognizes your friends or can even identify all of your coworkers!

You can really impress your boss with this one. Surprise them one day with an app that calls out your coworkers by name every time they walk by your desk. 😉

Please note: The VIP coupon will work only for the next month (ending May 1, 2020). It’s unknown whether the VIP period will renew after that time.

After that, although the VIP content will be removed from Udemy, all who purchased the VIP course will get permanent free access on deeplearningcourses.com.

Minimal Prerequisites

This course is designed to be a beginner to advanced course. All that is required is that you take my free Numpy prerequisites to learn some basic scientific programming in Python. And it’s free, so why wouldn’t you!?

You will learn things that took me years to learn on my own. For many people, that is worth tens of thousands of dollars by itself.

There is no heavy math, no backpropagation, etc. Why? Because I already have courses on those things. So there’s no need to repeat them here, and PyTorch doesn’t use them. So you can relax and have fun. =)

Why PyTorch?

All of my deep learning courses until now have been in Tensorflow (and prior to that Theano).

So why learn PyTorch?

Does this mean my future deep learning courses will use PyTorch?

In fact, if you have traveled in machine learning circles recently, you will have noticed that there has been a strong shift to PyTorch.

Case in point: OpenAI switched to PyTorch earlier this year (2020).

Major AI shops such as Apple, JPMorgan Chase, and Qualcomm have adopted PyTorch.

PyTorch is primarily maintained by Facebook (Facebook AI Research to be specific) – the “other” Internet giant who, alongside Google, have a strong vested interest in developing state-of-the-art AI.

But why PyTorch for you and me? (aside from the fact that you might want to work for one of the above companies)

As you know, Tensorflow has adopted the super simple Keras API. This makes common things easy, but it makes uncommon things hard.

With PyTorch, common things take a tiny bit of extra effort, but the upside is that uncommon things are still very easy.

Creating your own custom models and inventing your own ideas is seamless. We will see many examples of that in this course.

For this reason, it is very possible that future deep learning courses will use PyTorch, especially for those advanced topics that many of you have been asking for.

Because of the ease at which you can do advanced things, PyTorch is the main library used by deep learning researchers around the world. If that’s your goal, then PyTorch is for you.

In terms of growth rate, PyTorch dominates Tensorflow. PyTorch now outnumbers Tensorflow by 2:1 and even 3:1 at major machine learning conferences. Researchers hold that PyTorch is superior to Tensorflow in terms of the simplicity of its API, and even speed / performance!

Do you need more convincing?

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[VIP COURSE UPDATE] Artificial Intelligence: Reinforcement Learning in Python

March 18, 2020

Artificial Intelligence: Reinforcement Learning in Python

VIP Promotion

Hello all!

In this post, I am announcing the VIP coupon to my course titled “Artificial Intelligence: Reinforcement Learning in Python”.

There are 2 places to get the course.

  1. Udemy, with this VIP coupon: https://www.udemy.com/course/artificial-intelligence-reinforcement-learning-in-python/?couponCode=REINFORCEVIP2 (expires Aug 17, 2021)
  2. Deep Learning Courses (coupon automatically applied): https://deeplearningcourses.com/c/artificial-intelligence-reinforcement-learning-in-python

You may recognize this course as one that has already existed in my catalog – however, the course I am announcing today contains ALL-NEW material. The entire course has been gutted and every lecture contained within the course did not exist in the original version.

One of the most common questions I get from students in my PyTorch, Tensorflow 2, and Financial Engineering courses is: “How can I learn reinforcement learning?”

While I do cover RL in those courses, it’s very brief. I’ve essentially summarized 12 hours of material into 2. So by necessity, you will be missing some things.

While that serves as a good way to scratch the surface of RL, it doesn’t give you a true, in-depth understanding that you will get by actually learning each component of RL step-by-step, and most importantly, getting a chance to put everything into code!

This course covers:

  • The explore-exploit dilemma and the Bayesian bandit method
  • MDPs (Markov Decision Processes)
  • Dynamic Programming solution for MDPs
  • Monte Carlo Method
  • Temporal Difference Method (including Q-Learning)
  • Approximation Methods using Radial Basis Functions
  • Applying your code to OpenAI Gym with zero effort / code changes
  • Building a stock trading bot (different approach in each course!)

 

When you get the DeepLearningCourses.com version, note that you will get both versions (new and old) of the course – totalling nearly 20 hours of material.

If you want access to the tic-tac-toe project, this is the version you should get.

Otherwise, if you prefer to use Udemy, that’s fine too. If you purchase on Udemy but would like access to DeepLearningCourses.com, I will allow this since they are the same price. Just send me an email and show me your proof of purchase.

Note that I’m not able to offer the reverse (can’t give you access to Udemy if you purchase on DeepLerningCourses.com, due to operational reasons).

So what are you waiting for?

 

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Predicting Stock Prices with Facebook Prophet

August 3, 2021

Prophet is Facebook’s library for time series forecasting. It is mainly geared towards business datasets (e.g. predicting adspend or CPU usage), but a natural question that comes up with my students whenever we talk about time series is: “can it predict stock prices?”

In this article, I will discuss how to use FB Prophet to predict stock prices, and I’ll also show you what not to do (things I’ve seen in other popular blogs). Furthermore, we will benchmark the Prophet model with the naive forecast, to check whether or not one would really want to use this.

Note: This is an excerpt from my full VIP course, “Time Series Analysis, Forecasting, and Machine Learning“. If you want the code for this example, along with many, many other code examples on stock prices, sales data, and smartphone data, get the course!

The Prophet section will be part of the VIP version only, so get it now while the VIP coupon is still active!

 

How does Prophet work?

The Prophet model is a 3 component, non-autoregressive time series model. Specifically:

$$y(t) = g(t) + s(t) + h(t) + \varepsilon(t)$$

 

The Prophet model is not autoregressive, like ARIMA, exponential smoothing, and the other methods we study in a typical time series course (including my own).

The 3 components are:

1) The trend \( g(t) \) which can be either linear or logistic.

2) The seasonality \( s(t) \), modeled using a Fourier series.

3) The holiday component \( h(t) \), which is essentially a one-hot vector “dotted” with a vector of weights, each representing the contribution from their respective holiday.

 

How to use Prophet for predicting stock prices

In my course, we do 3 experiments. Our data is Google’s stock price from approximately 2013-2018, but we only use the latter 2 years as training data.

The first experiment is “plug-and-play” into Prophet with the default settings.

 

Here are the results:

Unfortunately, Prophet mistakenly believes there is a weekly seasonal component, which is the reason for the little “hairs” in the forecast.

When we plot the components of the model, we see that Prophet has somehow managed to find some weekly seasonality.

Of course, this is completely wrong! The model believes that the stock price increases on the weekends, which is highly unlikely because we don’t have any data for the weekend.

 

The second experiment is an example of what not to do. I saw this in every other popular blog, which is yet another “data point” that should convince you not to trust these popular data science blogs you find online (except for mine, obviously).

In this experiment, we set daily_seasonality to True in the model constructor.

 

Here are the results.

It seems like those weird little “hairs” coming from the weekly seasonal component have disappeared.

“The Lazy Programmer is wrong!” you may proclaim.

However, this is because you may not understand what daily seasonality really means.

Let’s see what happens when we plot the components.

This plot should make you very suspicious. Pay attention to the final chart.

“Daily seasonality” pertains to a pattern that repeats everyday with sub-daily changes.

This cannot be the case, because our data only has daily granularity!

Lesson: don’t listen to those “popular” blogs.

 

For experiment 3, we set weekly seasonality to False. Alternatively, you could try playing around with the priors.

 

Here are the results.

Notice that the “little hairs” are again not present.

 

Is this model actually good?

Just because you can make a nice chart, does not mean you have done anything useful.

In fact, you see the exact same mistakes in those blog articles and terrible Udemy courses promising to “predict stock prices with LSTMs” (which I will call out every chance I get).

One of the major mistakes I see in nearly every blog post about predicting stock prices is that they don’t bother to compare it to a benchmark. And as you’ll see, the benchmark for stock prices is quite a low bar – there is no reason not to compare.

Your model is only useful if it can beat the benchmark.

For stock price predictions, the benchmark is typically the naive forecast, which is the optimal forecast for a random walk.

Random walks are often used as a model for stock prices since they share some common attributes.

For those unfamiliar, the naive forecast is simply where you predict the last-known value.

Example: If today’s price on July 5 is $200 and I want to make a forecast with a 5-day horizon, then I will predict $200 for July 6, $200 for July 7, …, and $200 for July 10.

I won’t bore you with the code (although it’s included in the course if you’re interested), but the answer is: Prophet does not beat the naive forecast.

In fact, it does not beat the naive forecast on any horizon I tried (5 days, 30 days, 60 days).

Sidenote: it’d be a good exercise to try 1 day as well.

 

How to learn more

Are stock prices really random walks? Although this particular example provides evidence supporting the random walk hypothesis, in my course, the GARCH section will provide strong evidence against it! Again, it’s all explained in my latest course, “Time Series Analysis, Forecasting, and Machine Learning“. Only the VIP version will contain the sections on Prophet, GARCH, and other important tools.

The VIP version is intended to be limited-time only, and the current coupon expires in less than one month!

Get your copy today while you still can.

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Why do you need math for machine learning and deep learning?

July 9, 2021

In this article, I will demonstrate why math is necessary for machine learning, data science, deep learning, and AI.

Most of my students have already heard this from me countless times. College-level math is a prerequisite for nearly all of my courses already.

This article is a bit different.

Perhaps you may believe I am biased, because I’m the one teaching these courses which require all this math.

It would seem that I am just some crazy guy, making things extra hard for you because I like making things difficult.

WRONG.

You’ve heard it from me many times. Now you’ll hear it from others.

This article is a collection of resources where people other than myself explain the importance of math in ML.

 

Example #1

Let’s begin with one of the most famous professors in ML, Daphne Koller, who co-founded Coursera.

In this clip, Lex Fridman asks what advice she would have for those interested in beginning a journey into AI and machine learning.

One important thing she mentions, which I have seen time and time again in my own experience, is that those without typical prerequisite math backgrounds often make mistakes and do things that don’t make sense.

She’s being nice here, but I’ve met many of these folks who not only have no idea that what they are doing does not make sense, they also tend to be overly confident about it!

Then it becomes a burden for me, because I have to put in more effort explaining the basics to you just to convince you that you are wrong.

For that reason, I generally advise against hiring people for ML roles if they do not know basic math.

 

Example #2

I enjoyed this strongly worded Reddit comment.

Original post:

Top comment:

 

Example #3

Not exactly machine learning, but very related field: quant finance.

In fact, many students taking my courses dream about applying ML to finance.

Well, it’s going to be pretty hard if you can’t pass these interview questions.

http://www.math.kent.edu/~oana/math60070/InterviewProblems.pdf

Think about this logically: All quants who have a job can pass these kinds of interview questions. But you cannot. How well do you think you will do compared to them?

 

Example #4

Entrepreneur and angel investor Naval Ravikant explains why deriving (what we do in all of my in-depth machine learning courses) is much more important than memorizing on the Joe Rogan Experience.

Most beginner-level Udemy courses don’t derive anything – they just tell you random facts about ML algorithms and then jump straight to the usual 3 lines of scikit-learn code. Useless!

Link: https://www.youtube.com/watch?v=3qHkcs3kG44&t=5610s (Skips to 1:33:30 automatically)

 

This article will be updated over time. Keep checking back!

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Time Series: How to convert AR(p) to VAR(1) and VAR(p) to VAR(1)

July 1, 2021

This is a very condensed post, mainly just so I could write down the equations I need for my Time Series Analysis course. 😉

However, it you find it useful – I am happy to hear that!

[Get 75% off the VIP version here]

Start with an AR(2):

$$ y_t = b + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \varepsilon_t $$

 

Suppose we create a vector containing both \( y_t \) and \( y_{t -1} \):

$$\begin{bmatrix} y_t \\ y_{t-1} \end{bmatrix}$$

 

We can write our AR(2) as follows:

$$\begin{bmatrix} y_t \\ y_{t-1} \end{bmatrix} = \begin{bmatrix} b \\ 0 \end{bmatrix} + \begin{bmatrix} \phi_1 & \phi_2 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} y_{t-1} \\ y_{t-2} \end{bmatrix} + \begin{bmatrix} \varepsilon_t \\ 0 \end{bmatrix}$$

 

Exercise: expand the above to see that you get back the original AR(2). Note that the 2nd line just ends up giving you \( y_{t-1} = y_{t-1} \).

The above is just a VAR(1)!

You can see this by letting:

$$ \textbf{z}_t = \begin{bmatrix} y_t \\ y_{t-1} \end{bmatrix}$$

$$ \textbf{b}’ = \begin{bmatrix} b \\ 0 \end{bmatrix} $$

$$ \boldsymbol{\Phi}’_1 = \begin{bmatrix} \phi_1 & \phi_2 \\ 1 & 0 \end{bmatrix} $$

$$ \boldsymbol{\eta}_t = \begin{bmatrix} \varepsilon_t \\ 0 \end{bmatrix}$$.

Then we get:

$$ \textbf{z}_t = \textbf{b}’ + \boldsymbol{\Phi}’_1\textbf{z}_{t-1} + \boldsymbol{\eta}_t$$

Which is a VAR(1).

 

Now let us try to do the same thing with an AR(3).

$$ y_t = b + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \phi_3 y_{t-3} + \varepsilon_t $$

 

We can write our AR(3) as follows:

$$\begin{bmatrix} y_t \\ y_{t-1} \\ y_{t-2} \end{bmatrix} = \begin{bmatrix} b \\ 0 \\ 0 \end{bmatrix} + \begin{bmatrix} \phi_1 & \phi_2 & \phi_3 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} y_{t-1} \\ y_{t-2} \\ y_{t-3} \end{bmatrix} + \begin{bmatrix} \varepsilon_t \\ 0 \\ 0 \end{bmatrix}$$

Note that this is also a VAR(1).

 

Of course, we can just repeat the same pattern for AR(p).

 

The cool thing is, we can extend this to VAR(p) as well, to show that any VAR(p) can be expressed as a VAR(1).

Suppose we have a VAR(3).

$$ \textbf{y}_t = \textbf{b} + \boldsymbol{\Phi}_1 \textbf{y}_{t-1} + \boldsymbol{\Phi}_2 \textbf{y}_{t-2} + \boldsymbol{\Phi}_3 \textbf{y}_{t-3} + \boldsymbol{ \varepsilon }_t $$

 

Now suppose that we create a new vector by concatenating \( \textbf{y}_t \), \( \textbf{y}_{t-1} \), and \( \textbf{y}_{t-2} \). We get:

$$\begin{bmatrix} \textbf{y}_t \\ \textbf{y}_{t-1} \\ \textbf{y}_{t-2} \end{bmatrix} = \begin{bmatrix} \textbf{b} \\ 0 \\ 0 \end{bmatrix} + \begin{bmatrix} \boldsymbol{\Phi}_1 & \boldsymbol{\Phi}_2 & \boldsymbol{\Phi}_3 \\ I & 0 & 0 \\ 0 & I & 0 \end{bmatrix} \begin{bmatrix} \textbf{y}_{t-1} \\ \textbf{y}_{t-2} \\ \textbf{y}_{t-3} \end{bmatrix} + \begin{bmatrix} \boldsymbol{\varepsilon_t} \\ 0 \\ 0 \end{bmatrix}$$

This is a VAR(1)!

 

 

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Coding Interview Questions – Bioinformatics Rosalind.info – Finding a motif in DNA (Episode 18)

May 4, 2021

Hello all!

In this video, we’re going to do another coding interview question where I walk you through the process of:

– explaining the problem

– solving the problem

– analyzing the time complexity of the solution

These videos are designed to help you practice for future job interviews where you are required to answer technical whiteboard problems.

The problem we’ll solve can be viewed as a bioinformatics problem, but you don’t have to know anything about biology! Even those who only know basic coding should be able to solve this problem.

I hope this motivates you to realize that “bioinformatics” is not all that different from what you already know how to do – and therefore, contributing to this important and exciting field is totally within your reach.

Click here to watch –> https://youtu.be/cGEcwVmcD50

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