Expert Answer:Math Discussion Reply (300 – 400 words)

  

Solved by verified expert:Please replay to four (4) of my classmate posts each one in 75 – 100 wordsI attached my friend post and some example on how to make reply.
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One skill or concept from the time series studies that I understand well is the moving
average. What helped me understand it more was creating a table in Excel, inserting the
basic formulas to assist with the calculations, and then observing the impact as I
increased and decreased the period count. By performing that exercise and then graphing
my findings, I could easily see how adding more periods “smoothed out” the variability in
the lines, while decreasing the period count made the moving averages more responsive
to changes.
I’ve inserted a visual of the broader stock market (S&P 500) and overlaid three different
moving averages: the 20-day, the 50-day, and the 200-day. As you can see in the graph,
the 20-day (green line) is very responsive to price changes in the market, while the 200day (red line) is slower to respond and suppresses some of the noise and volatility
associated with the daily price changes.
I wanted to jump on this thread about moving averages to ask some questions, not
because I don’t understand the topic but am looking for some more clarity.
With the idea of moving averages I understand the concept and that the higher count
you use when performing the moving average the less noise that is visible. In Geralds
example the 20-day count follows along with the data and shows the volatility in the
market, whereas the 200 day count smooths the data and removes the noise.
Over the short term I can see the advantages with using a moving average to get a better
perspective on the data. Specifically this is very helpful when looking at the market,
which is very volitile in the short term but usually shows long term steady growth.
Would it be appropriate to use moving averages for looking at very long term time series?
What if we were looking at the 2008 recession and were to smooth it? Would this be a
good thing to do? What are the advantages with omitting the large decreases?
Hey there, Patrick. You’ve asked some great questions!
When it comes to evaluating a stock chart using moving averages, I think there is value
in using a variety of different time frames so you can fully capture the price action. For
example, that same application (StockCharts.com) that I used in the visual above allows
you to view the price action across a wide variety of time frames. You can look at intraday price movement, and you can also look at price movement over the last 10
years. You can also look at daily price action, weekly price action, and monthly price
action as captured by the individual candlesticks on the chart; these can all be controlled
by the charting software.
Irrespective of the time frame you use, the moving averages are indications of a trend; the
moving averages with lower period counts show shorter trends, while the ones with
higher period counts show longer-term trends. The 2008 decline was so severe that it
actually altered even the longer term moving averages. Depending on your time horizon
as an investor, you can select which moving average you’d like to use as an indicator.
I also think it’s worth noting that moving averages are LAGGING indicators; they are
based on previous price action. So I don’t think they should be relied on too heavily as a
predictive element. There are other indicators like the RSI and Bollinger Bands that can
be pretty reliable for identifying extreme conditions (multiple standard deviations) that
may revert to their mean.
Manage Discussion Entry
Gerald,
Thank you fore getting back to my questions and further explaining the concepts of
moving averages in relation to the market data you put forward. I really appreciated you
detailed and well researched ideas on the subject.
I must also say thank-you to the people further down in this thread, and I think that it
has lead to a nice discussion about the concepts of time series analysis, moving average
calculations, and exponential smoothing.
Thanks,
DE
There are various concepts from time series studies, stationarity and autoregressive that
have been having to acquire from the previous classes and exercises. However, the
moving average (MA) concept has been a little bit challenging for me to understand and
thus unable to acquire adequate skills from moving average as far as time series is
concerned. Lack of enough practical exercises on theoretical work in creating tables in
excel and not familiarizing myself with formulas and functions to perform statistical
calculations has contributed to a slow understanding of this concept.
Therefore, due to the lack of adequate understanding of this the moving average concept,
I would like to pose several questions that will enhance a better understanding. First, can
the moving average concept be a valuable analytical tool to conclude from, especially for
volatile data? Second, what the functions of moving average, when is it used and when is
not used? Is this concept more effective when combining with other ideas like
autoregressive than when relied on solely? Apart from accurately indicating price trends,
what are its other applications in real life situations?
Gerald,
I found Ch. 8 to be my favorite chapter thus far. I enjoyed learning about time series, and
moving averages were actually, dare I say, fun to calculate! It’s quite interesting, as you
illustrated, to see that changing the number of periods can drastically change the curve
and tell a totally different story. Your 20-day average line makes the S&P look fairly
volatile from October onward, whereas the 200-day average looks more like a plateau
that might suggest the S&P making a correction or simply leveling out. This shows the
importance of filtering through the “noise” in the data and seeing the big picture, but
that’s not to say that the short term fluctuations aren’t important.
Tristan
Gerald,
This was one topic I found quite interesting and fun as well. This graph does a great job of
illustrating the differences in moving averages of different time lengths which helps
show why they are so important and powerful. Moving averages can be so important in
seeing a bigger picture of what is going on with the data.
Hi Gerald,
Thanks for adding a visual to better describe what you have learned. The moving average
is an interesting concept, and one that takes time and visualisation in order to better
understand. I think that looking at a time series within excel is a good way to tackle the
subject. Smoothing out a graph is another skill / topic that I understand much better after
this week’s module. I think our group project 4 really helped me to understand that.
When we looked at e-commerce sales in relation to time series, the graph really told a
story!
Thanks for further elaborating on these topics.
Best,
Krista
Hi Gerald,
I think the graph that you chose is an excellent visualization between different period
counts within a moving average calculation. It definitely helped me gain a better
understanding of the usefulness of moving average calculations.
Hope the term is going well for you.
Cheers,
Turner
Gerald,
Thank you for your post. I always enjoy reading your posts during these discussions. This
explanation like others have helped me understand things more in this class. It is one
thing to learn from a teacher and the book, but learning from other students helps me out
a lot sometimes just to see it explained one other time.
Thank you.
Hi Gerald,
Great post, the visual between the different period moving averages definitely help me
grasp the concept much better. Thank you.
Moving averages are something that I’ve really struggled with especially on the
homework assignments. I think I understand calculations of the moving averages but I
had don’t quite understand what the point of a moving average is. I also had problems
trying to calculate the mean standard error for the moving averages, which I think is just
related to the fact that I don’t quite understand the idea of moving averages.
Roman,
I think the main point of a moving average is that it becomes more accurate than a static
average. You should check out Gerald’s post at the top of the page as he does a great job
of showing and explaining. The moving average combines a number of averages to create
the graph we are used to seeing. Where this can be especially useful is in comparing a
small timeframe worth of data with a much longer moving average. This can help
identify if our smaller sample is actually representative of the larger average.
Hi Roman. I consider the point of the moving average (MA) to be a tool that helps
smooth out data values by filtering out the “noise” from short-term value
fluctuations. I’d say that the most common application for moving averages on a graph is
to help identify the trend direction. For example, if you take a look at the visual I posted
above, you can see that in early October, the stock market took a leg down. During that
period, the 20-day MA dipped lower, the 50-day MA was trending horizontally, and the
200-day MA was still moving higher. We can loosely interpret this to mean that in early
October, the short-term trend was lower, the mid-range trend was horizontal, and the
longer-term trend was still higher.
Roman,
Moving averages take into consideration last data as a way to smooth out large variations
in the data point to point. This is a way to get a better picture of the general trends that
are hidden within very volatile data. If you have a consistent average and then an
extreme outlier or point that sits far above or below the others, a moving average would
help to dampen this volatility.
Thanks for your questions!
– Drew
I feel like one skill that I am struggling with is exponential smoothing. I understand the
context of using it, but the calculations are confusing me as to where I need to do certain
things. After watching the video this week I think that it is also due to the fact that I am
still unsure about the weighted average if I calculate that right or not.
Hi Nathan,
You’re not the only one who is struggling with exponential smoothing calculations. I
understand how to use the calculations in excel, but I don’t have the best grasp on how
the calculation works. I feel like I have a better understanding of moving averages
compared to exponential smoothing because moving averages have a defined interval /
period.
Best of luck,
Turner
I would have to say that one concept that I have started to appreciate is the moving
average concept, and how the visualization between a 30 day moving average and a 365
day moving average can portray rather different statistical trends.
Notice that with the larger intervals, the trend lines tend to smooth out and reduce
fluctuating data. Separating different intervals between a moving average helps paint a
better picture than adding a line of best-fit because they still have data points and are not
straight lines. I do however am still learning the details of time series calculations, but the
visualizations created are very helpful.
Turner,
Thank you for showing the graph that you made for a moving average. I will use this as
something to help me create my graphs that way I can get a general idea.
Turner,
Moving averages are a concept that I kind of struggled with before but post such as yours
have really made me appreciate and gain a much better understanding of the concept.
Great post, thank you.
Skills I have acquired about stationarity concept in time series studies are fundamental in
real life application situations. Through doing practical exercises not only for class work
but also for statistical competition, forums have contributed to gaining a deeper
understanding of time series concept. Stata and R studio are the tools that I have been
using, and they have helped in acquiring the knowledge about time series due to their
simplicity and ease of use to find mean, variance and outputting graphs and pie charts for
analysis purposes.
What has made me wrap the stationarity concept around my head is the fact that
statistical properties can be predicted to similar in the future as they have been in the
past. Also, the predictions made can be untransformed by use of whichever mathematical
formula used to obtain the projections. This concept is mostly used in business firms to
predict future their performance as well as their past and current position.
Stationarity is a fundamental concept of time series studies I have been observing and
using when giving reports of given data from different companies as a data analyst
assistant.
Hi Fares
I agree with you that these skills we are learning in this week’s module are very much
relevant / fundamental in every day life. I know that I will see a time series graph and be
able to read it clearly. I will also be able to read the data in a objective and subjective
way. I know that these graphs can easily be skewed. I think that the “smoothing” of the
time series graph was another great skill we learned this week.
Thanks for sharing your opinion, I very much agree with your post.
Krista
Fares,
Great post. I’ve found this chapter’s information to be the most interesting in this class,
and I can absolutely see applying this information practically in the future. Stationarity as
a concept reminds me of something I learned in a meteorology class about persistence
forecasting. Meteorologists use past data from previous years to make predictions in the
long-range forecast, such as day 10 of a 10 day forecast. They don’t have a clue what the
weather will actually look like in 10 days, as weather systems move and change quickly,
but they can average the historical data for that date and give a prediction based on the
concept of stationarity of what the weather will do that day.
Regards,
Tristan
Something that I am currently struggling to fully understand is the cengage homework
we had due last weekend. More specifically question #3 which I will leave here to see if
someone can show me the steps to get the final answers. I tried it multiple times and
never seemed to get it correct. I am the most confused about the second part of B.
Thanks!
Hi Daniela,
Have you tired using excel to complete these problems? I can’t help on this exact
problem, but I will say that once I started using excel while completing my cengage
homework I found that it was much easier to do the math and work with the formulas. I
just copy the data in to Excel and use the correct formula. It also helps, when you save
the excel sheet, and you can go back and use the formula if you need it! Just a suggestion
– hope it helps.
Krista
Daniela,
That question can be tricky, but use Excel like Krista said!
For the forecasts, you’re averaging all of the values for the previous periods, so the
prediction for week 2 will be the value for week 1, the prediction for week 3 will be the
values for weeks 1 and 2 divided by 2, week 4 will be the values for 1, 2, and 3 divided by
3 and so on. This will give your forecast for month 8. The MSE will be calculated like
usual- subtract the actual value from the forecasted value, square the differences and then
average the squares.
Best of luck!
Tristan

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