In this video lecture,
we'll talk about some time plots. So what are the objectives
of this video lecture? We will see some examples
of time series and we'll try to produce some
meaningful time plots. Those are the objectives of this lecture. We will look at a few time series
data from the package astsa, to be specific, we'll look at
the following data set that's titled jj, flu and so forth on astsa. I'm going to talk about
each one of them in detail. So first data said the time
shares we want to look at is the time series about the Johnson and
Johnson Quarterly Earnings. If the Johnson and Johnson is a US
company and we're going to look at the quarterly earnings for
84 quarters starting from 1964, the first quarter to 1980,
the last quarter. And it's titled jj in the package ASA. At this point I'll assume that
you have already installed package called ASOS Toyer Machine. If you have not done refer to
one of the videos where Bill is talking about installing those
packages on to your own machine. I'm just going to use
that package also now. So I'm just going to use require Astsa so
that I can use it. Now that I have asta in my shell,
I'm going to look at this documentation and the documentation says
that this includes data and scripts that accompany to the book by and
Stoffer. We'll be looking at the quarterly
earnings of Johnson and Johnson. The data set, the timesheet is called jj. If I just say help(jj), documentation
says that this is Johnson and Johnson quarterly earnings per share. It's collected 21 years
starting from 1960 to 1980. It is already a time sense object. Which means I do not use
to use this TS routine or TS operator to make
the data a time series. So, it is already a time series. It already starts upon 1960. So all I have to do is basically
put some meaningful title and x label and y label into my plot command. So basically here what I have is that I'm
going to plot jj, since jj is already a time series object,
I do not need to write this plot.ts. And I'm going to use type o, which means every point in the time series
will have a little circle on it and the title I put is the Johnson&Johnson
quarterly earnings per share, this is a string that goes into the main,
that becomes a title. For the y axis label we put,
let's say earnings, and x label If I once come in,
I will obtain this time plot. And I have nice title, y label, x label. This first step in analysis
of a time series is basically to produce the point plot, because by just looking at the time plot,
it gives you an idea of what's going on. By just looking at this time plot,
I would say there's some kind of trend Throughout the years, so definitely
there's an increase throughout the years. I can see the trend, but
I can also see fluctuations, the seasonal variations on that trend. So there is a seasonal
effect in this time series. There is some kind of a trend, but one
other thing I realize is the following. At the beginning,
my time series data At the beginning the variation is not that much.But
the leg room I have a higher variations. Now later on we will see that if
we have a transitional affect or if you have a different variation
different parts of the time series. It actually violates so-called stationary
principle, which I will talk about next For now, we'll produce the time plot,
we have an idea what's going on. Next time series is about pneumonia and
influenza. That's in the US from 1968 to 1978,
so this is a 11 year period. And they basically recorded
the monthly deaths per 10,000 people. So this data is called flu
with ASA at the time series. Let's look at the time plot. Before I do that I am
going to say health flu so that I can get an idea of I can get
the documentation about this flu. It actually says the monthly Pneumonia and influenza deaths in
the US from 1968 to 1978. And it is per, that's number of deaths
per 10,000 people monthly for 11 years. It is already a time
series object which means I do not have to deal with
ts operator here either. And it starts from 1968. It ends at 1979. Flu, The plot flu data. And I put the sum title. And a y label, an x label. And we obtained the following time plot. In this time plot, we see that there
is some kind of seasonality going on. There is a peak every after year or so. And that kind of shows that
there is some kind of systality going on in this data which is
definitely not a stationary time series which I will talk
about in the next lecture. But if you look at the over all trend,
there might be a trend that overall number of tasks going
down which might hard to see. But okay, so
this is the time plot for flu data. The next time stretch we're going
to look at is called globtemp. It is about land-ocean temperature. The global mean land-ocean temperature and
they're recorded how much land-ocean global temperature, mean temperature,
is deviating from some base temperature. And that base temperature is taking
the average from 1951 til 1980. So that's our average. That's our base temperature. And we'll look at the deviations
from that temperature and data is collected from 1880 til 2015. And the source is actually NASA. So I say plot globtemp and
I put a title and the y label, an x label and I plot it. I see time plot. Basically from this time plot
my first impression is that there is some kind of trend. So temperature deviations are going up. And even though there is a trend, there's
some kind of seasonality on that trend as well, probably,
because of the seasons of the year. Next time series is the land
only temperature deviations, so this idea is the same. It is between 1880 to 2015. It is a game temperature deviations
which is measured in centigrade from the base temperature. But this is for lab only. So go ahead at this point try to obtain
your own meaningful time plot for the data set called global temp L in ASA. The last time series that we'll look
in this lecture is called Star. It is about the magnitude of a star
at midnight which is collected for 600 consecutive days. This data is from ASA packet, but
if you look at the documentation using the health star, it is actually from
the book by Whittaker and Robinson called The Calculus of Observations,
a Treatise on Numerical Mathematics. So we plot star data,
and y label and x label, and we opting following,
time plot which definitely shows us there is some kind
of seasonality going on. We can see some periodicity
in this time plot. So what have you learned in this lecture? You have learned that time series exist
in a variety of areas starting from financial world,
ended up with astrophysics. And you have learned how to
produce meaningful time plots.