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Now we are going to discuss a particular type of series which is known as a random walk.

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It is also known as Drunkard Walk, which is why, to explain this concept, we have images of drunk

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characters here.

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Suppose this character is standing at this particular point in this glove in the beginning.

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Can we guess where this person will be after taking 10 steps?

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The dotted but shown here is one of the infinitely many parts that this character can take.

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The point is that for a person who is randomly taking steps in any direction, it is hard to make a

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forecast of that person's location.

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Only thing we can say is that the next step of that person will somewhere be near the previous location.

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So if previous location is this point, then the new location can only be one step away from this point.

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This is the concept behind random walk.

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The next value of a random Walk Time series has a literal dependence on the previous value.

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And apart from that dependence, this series is completely random.

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I hope you understand when at times it is becomes a random walk.

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But why did we discuss this?

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As I told you about white noise, a white noise.

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Times it is is completely unpredictable.

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However, in a random walk, there is a small part which we know that is, it is close to the last value

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of the times d the rest of it is completely random.

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Now think about it.

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If you want to forecast the next value of the series, which is a random walk.

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What will be your prediction?

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If you said that this last value is your prediction for next value, then you are absolutely right.

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Although we know with almost certainty that it is not going to be this lost value in the next step of

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the times.

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It is, but it is our best bet to stay close to the unknown random new value.

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So when a series is a random walk, we use previous value as the forecast for the next value.

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This is also called naive forecasting for a random walk.

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None of the advanced models can give you better prediction accuracy than naive forecasting.

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In fact, name forecasting accuracy serves as a benchmark for all the other models also.

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So during our practical classes, you will notice that we will often find the forecasts accuracy also

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so that we can actually compare the performance of our advanced models.

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When we compare this accuracy, if the accuracy of our advanced model is better than the accuracy of

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naïf forecast, then our model is finding out more information and we can say that the underlying series

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is not a random walk.

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But if other advanced model is not able to get better accuracy than an April cost, then probably the

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underlying series is a random walk.

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And that is why I did once model is not able to get more information out of that cities.

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I'll just summarize the concept here.

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If you have a white noise time cities, you cannot forecast at all.

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If you have a random walk times, it is my forecast.

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Is your best forecast.

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And for all the other cities which have more information in them, we will see the advanced models of

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forecasting for such cities in the coming sections.