Now we are going to discuss a particular type of series which is known as a random walk.
It is also known as Drunkard Walk, which is why, to explain this concept, we have images of drunk
characters here.
Suppose this character is standing at this particular point in this glove in the beginning.
Can we guess where this person will be after taking 10 steps?
The dotted but shown here is one of the infinitely many parts that this character can take.
The point is that for a person who is randomly taking steps in any direction, it is hard to make a
forecast of that person's location.
Only thing we can say is that the next step of that person will somewhere be near the previous location.
So if previous location is this point, then the new location can only be one step away from this point.
This is the concept behind random walk.
The next value of a random Walk Time series has a literal dependence on the previous value.
And apart from that dependence, this series is completely random.
I hope you understand when at times it is becomes a random walk.
But why did we discuss this?
As I told you about white noise, a white noise.
Times it is is completely unpredictable.
However, in a random walk, there is a small part which we know that is, it is close to the last value
of the times d the rest of it is completely random.
Now think about it.
If you want to forecast the next value of the series, which is a random walk.
What will be your prediction?
If you said that this last value is your prediction for next value, then you are absolutely right.
Although we know with almost certainty that it is not going to be this lost value in the next step of
the times.
It is, but it is our best bet to stay close to the unknown random new value.
So when a series is a random walk, we use previous value as the forecast for the next value.
This is also called naive forecasting for a random walk.
None of the advanced models can give you better prediction accuracy than naive forecasting.
In fact, name forecasting accuracy serves as a benchmark for all the other models also.
So during our practical classes, you will notice that we will often find the forecasts accuracy also
so that we can actually compare the performance of our advanced models.
When we compare this accuracy, if the accuracy of our advanced model is better than the accuracy of
naïf forecast, then our model is finding out more information and we can say that the underlying series
is not a random walk.
But if other advanced model is not able to get better accuracy than an April cost, then probably the
underlying series is a random walk.
And that is why I did once model is not able to get more information out of that cities.
I'll just summarize the concept here.
If you have a white noise time cities, you cannot forecast at all.
If you have a random walk times, it is my forecast.
Is your best forecast.
And for all the other cities which have more information in them, we will see the advanced models of
forecasting for such cities in the coming sections.