A third challenge that we often try

to implement over time series data is to search for motifs.

So, motifs are essentially repeating patterns.

So, in these three time series,

you will see that there are certain repeating patterns.

For example, this pattern here is repeating pretty regularly in this example,

and we see that basically the similar pattern also

repeats on the other time series as well.

We see that the same pattern here also repeats maybe a little bit less strongly,

but also on the third time series as well.

So, the question essentially becomes,

can we find these repeating patterns and can we explain them?

Because these repeating patterns for many applications

may signal certain events or certain important occurrences.

In this case for example,

these repeating patterns seem to correspond to the New Year time frame,

Christmas/New Year's time frame.

Right. So, in this case,

we can observe the repeating pattern and we can also explain the repeating pattern.

So, the question essentially becomes,

if you give me another dataset which shows different characteristic,

can we find these repeating patterns?

They are not always easy to find as in this example.

By the way, even basic on the web data,

it is not true that we'll have the pattern so easily identifiable.

For example, if you basically put in another sort of key term here,

in this case I select a time series and I track the interest on time series,

we see that there is a repeating pattern again,

but the repeating pattern is actually very different from

the repeating patterns of the first three search term.

So the question essentially becomes, an interesting question

becomes, why is that the case,

why are we seeing a different repeating pattern,

different motif for the search term time series over the other three search terms?

To be able to answer that,

the first thing that we need to do is,

we need to be able to locate

these repeating patterns in the time series, and we'll discuss that.

So, that will be one of the things that we will discuss in this unit. Finally-

Another important task that we would like to do

using time series data is classification of the time series.

Because time series usually Bayesian is used to record real-world events.

For example, we can use time series to record sensor positions.

In this case, there are certain sensors that are placed on the human body,

and you might be recording the physical positions of these of the sensors over time.

When we look at

the the time series recorded while the user is doing different actions for example,

walking and running, we can see that the time series are showing different patterns.

So, this time series here,

and this time series here,

the set of time series here are showing very different patterns.

So then essentially, the question becomes,

if you give me a new fresh time series that doesn't really tell has a label,

it doesn't tell me whether the user is walking,

it doesn't tell me the user is running,

it doesn't tell me the user is jumping,

can I look at the time series,

and can I classify the given time series as,

"Oh, the user is running,

oh the user is jumping,

or maybe the user is doing a mixture of those things", can I do that?

Classification is basically again an important problem, and once again,

it is one of the machine learning techniques that we are covering this program.

I'm not going to get into details of

the classification task as part of this video sequence,

but we have other videos that you can you can use especially for the classification task.

Okay. So, what is the overall goal?

So, we have introduced what the time series is.

We have looked at several important operations, important task,

important challenges that we face when using time series in data exploration,

and database decision- making.

So, one final important task that

I would like to introduce is time series modelling.

Essentially in this case,

we have a very specific task.

We are not necessary trying to compare different time series to each other,

we are not essentially trying to find repeating patterns in the time series,

we are not trying to classify the time series,

what we want to do is want to understand the time series.

Essentially, this is usually being formulated as,

can we discover a closed form formula,

and this formula is often called a model for time series,

that describes the given time series.

So, because if I can find a closed form formula for the given time series,

then I can have a better understanding of the time series.

Maybe I can forecast the future better.

We will see that this is a difficult task.

Finding a closed form formula for a given arbitrary time series is not easy.

So, a simpler problem which we will start from is,

can we characterize high level properties of a given time series?

We will see that this is going to be a little bit easier,

and we'll see that if we can characterize high level properties of a given time series,

it might help us actually find a formula for that time series.

So, in the next few slides,

we will basically discuss these high-level characteristics of time series,

or what the other type I will call here,

the types of time series.

So, now we are basically diving into the time-series data,

and we are trying to see how do different time series look,

and can I characterize them at a very high level?

That's what we try to do.

Okay. So, let's try to do that.

Let's start basically with the first simple type of time series.

The most simple types of time series is called Stationary Series.

This type of time series show similar pattern over time.

Now, similar pattern doesn't mean that it has the same values.

For example, this time series here wildly varies over time.

So, it doesn't show the same pattern,

the same value over time.

However, if we analyze the time series,

if you look at statistical properties such as the mean,

average value, the time series take over time.

If you look at the variance of the data over time,

we will see that that is essentially constant over time.

So, these type of series where the statistical properties are constant over time,

we call them Stationary Series.

The advantage of stationary series,

we will see them later, is that they are easy to analyze.

As the time series become more complex,

as the statistical properties of the time to change over time,

the time series becomes harder to study,

and it becomes harder to predict.

So, we'll basically call these as the Stationary Series.

The second type of series,

obviously, these are the Non-Stationary Series.

Right? So, in the case of non-stationary series,

the statistical properties of the time series changes over time.

They don't stay the same, they change over time.

I will basically say that there are different ways

for a time series to be non-stationary.

Okay? In this slide,

we see two different types of non-stationary behavior.

So, the first non-stationary behavior that we see here is cyclicity.

So, the blue time series here as you will see is cyclic.

So, it's mean changes over time.

So, the mean of this time series varies over time.

In this case, it varies through a periodic behavior,

it shows a periodic behavior.

So, we'll call this cyclic time series.

It turns out that in the real world,

many data shows cyclic behavior.

So, it's important for us to understand cyclicity,

and it's also important for us to understand how to capture,

how to discover, how to capture,

and how to use cyclic behavior.

The second type of non-stationarity is the trend.

Trend essentially, usually, it is used to mean a change,

a constant like change over time in the mean of the data.

In this case as you will see,

we have a cyclic data,

but the cyclic data also shows an increasing trend.

The data doesn't simply go up and down over time cyclically,

but it also has a positive trend,

the values are increasing over time.

Again, this data is non-stationary

because the statistical properties of the data changes over time.

Then once again, it is for many applications,

it is important to understand whether it shows a positive or negative trend.

So, we will need to be able to understand and characterize if

a time series shows non-stationary behaviors such as cyclicity or trend.

That's not all, because other things can also change over time.

In this case, we have again a cyclic data.

In fact we have two cyclic series,

but these series have a variance that is the spread of the data,

the variance which changes over time.

So, we have in this case,

the two datasets showing the same cyclicity,

but the variance of the data, the peaks,

the difference between the peaks of the data changes over time.

So, once again the question becomes,

can we discover these type of behaviors?

Can we represent these type of behaviors?

Can we use them to support decision-making?

So, this is the third type of non-stationary behavior.

Finally, again, I'm saying finally,

but I don't necessarily mean these are the only non-stationary behavior,

these are the only ones that will be essentially discussing in these slides.

The final type of non-stationary that we'll consider

is the change in the speed of the data.

That is, how fast the cycles do change.

In this example, the blue time series has a constant speed,

it is cyclic and the period of the cycles,

the frequency of the cycles stay the same over time.

On the other hand, for the red time series that we see here,

it is again cyclic.

It again has the same mean over time,

it again has the same variance over time,

but the frequency of the cycles,

the period of the cycles,

or the speed of the cycles change over time.

Once again, this is a non-stationary behavior.

Once again, when we are characterizing a time series,

we need to understand its speed.

The modal, the formula that you want to discover should have a way

to characterize the speed of the time series as well.

So, what did we discuss so far.

We have learned that some of the time series are stationary.

So, these time series show constant statistical properties.

Their mean and variance especially,

and also the speed are constant over time.

We also learned that not all time series are stationary.

Many time series and actual many times [inaudible] as in the real world are non-stationary.

Their statistical properties change over time.