An example, the time someone left home and the time someone called 9-1-1 and put these points in to predict ideally the time of incident on an excel format. I can put in a time in column a and column b but all it does is give me the half way point between the two. example column a says 12:00 and column b says 1:00 and the result would be 12:30. If I can get some thing more predictive using this approach, that is ideally what I'm looking for.
I used some of the standard functions in Excel to predict time based series.
We were looking at predicting data points for 1mis, 3mis and 6mis (mis = Months In Service).
We found that the forecast() function with some "fiddle" factors - sorry finely tuned polynomial assumptions - gave a reasonable prediction for our needs. We fed it steps of historical data to see the performance until it was suitable for what we needed.
I have the following 3 cases of a numeric metric on a time series(t,t1,t2 etc denotes different hourly comparisons across periods)
If you notice the 3 graphs t(period of interest) clearly has a drop off for image 1 but not so much for image 2 and image 3. Assume this is some sort of numeric metric(raw metric or derived) and I want to create a system/algo which specifically catches case 1 but not case 2 or 3 with t being the point of interest. While visually this makes sense and is very intuitive I am trying to design a way to this in python using the dataframes shown in the picture.
Generally the problem is how do I detect when the time series is behaving very differently from any of the prior weeks.
Edit: When I say different what I really mean is, my metric trends together across periods in t1 to t4 but if they dont and try to separate out of the envelope, that to me is an anomaly. If you notice chart 1 you can see t tries to split out from rest of the tn this is an anomaly for me. in other cases t is within the bounds of other time periods. Hope this helps.
With small data the best is if you can come up with a good transformation into a simpler representation.
In this case I would try the following:
Distance to the median along the time-axis. Then a summary of that, could be median, Mean-Squared-Error etc
Median of the cross-correlation of the signals
I want to calculate the probability of 6 independent events in excel. I know the general formula to do this howver it is very cumbersome to implement in excel.
Is there a better way?
The equation in your question suggests that you are asking for the probability of one or more of the events happening. This is the same as asking for the probability of "not none of them" happening. In Excel, you can calculate this using the following formula:
=1-PRODUCT(1-A1,1-A2,1-A3,1-A4,1-A5,1-A6)
(Here I am assuming that the probability of the events are given in cells A1:A6.)
However, if instead you are asking for the probability of all of the events happening, it's just the product of their individual probabilities:
=PRODUCT(A1,A2,A3,A4,A5,A6)
I have a mean value x and I want to model it into the future. I want to output a value of what it could be in 6 months. Assuming the value follows a normal distribution and we have the standard deviation how do I randomize the value x while following a normal distribution? I'm doing this in excel, but just understanding it would help too! Basically I want to produce numbers 68% of the time within 1 deviation, 95% of the time withing 2 deviation etc. etc.
You can use the excel function 'NORMINV' to convert a random input 'RAND()' to a normal distribution.
=NORMINV(RAND(),Mean,Std Dev)
i.e. if you repeat this many times, save and analyze the results, you'll see a bell curve over the input Mean value.
Does that get you started?
The tricky bit comes when you come up with the formula to predict what a value will be in the future using this.
We have a application where users enter prices all day. These prices are recorded in a table with a timestamp and then used for producing charts of how the price has moved... Every now and then the user enters a price wrongly (eg. puts in a zero to many or to few) which somewhat ruins the chart (you get big spikes). We've even put in an extra confirmation dialogue if the price moves by more than 20% but this doesn't stop them entering wrong values...
What statistical method can I use to analyse the values before I chart them to exclude any values that are way different from the rest?
EDIT: To add some meat to the bone. Say the prices are share prices (they are not but they behave in the same way). You could see prices moving significantly up or down during the day. On an average day we record about 150 prices and sometimes one or two are way wrong. Other times they are all good...
Calculate and track the standard deviation for a while. After you have a decent backlog, you can disregard the outliers by seeing how many standard deviations away they are from the mean. Even better, if you've got the time, you could use the info to do some naive Bayesian classification.
That's a great question but may lead to quite a bit of discussion as the answers could be very varied. It depends on
how much effort are you willing to put into this?
could some answers genuinely differ by +/-20% or whatever test you invent? so will there always be need for some human intervention?
and to invent a relevant test I'd need to know far more about the subject matter.
That being said the following are possible alternatives.
A simple test against the previous value (or mean/mode of previous 10 or 20 values) would be straight forward to implement
The next level of complexity would involve some statistical measurement of all values (or previous x values, or values of the last 3 months), a normal or Gaussian distribution would enable you to give each value a degree of certainty as to it being a mistake vs. accurate. This degree of certainty would typically be expressed as a percentage.
See http://en.wikipedia.org/wiki/Normal_distribution and http://en.wikipedia.org/wiki/Gaussian_function there are adequate links from these pages to help in programming these, also depending on the language you're using there are likely to be functions and/or plugins available to help with this
A more advanced method could be to have some sort of learning algorithm that could take other parameters into account (on top of the last x values) a learning algorithm could take the product type or manufacturer into account, for instance. Or even monitor the time of day or the user that has entered the figure. This options seems way over the top for what you need however, it would require a lot of work to code it and also to train the learning algorithm.
I think the second option is the correct one for you. Using standard deviation (a lot of languages contain a function for this) may be a simpler alternative, this is simply a measure of how far the value has deviated from the mean of x previous values, I'd put the standard deviation option somewhere between option 1 and 2
You could measure the standard deviation in your existing population and exclude those that are greater than 1 or 2 standard deviations from the mean?
It's going to depend on what your data looks like to give a more precise answer...
Or graph a moving average of prices instead of the actual prices.
Quoting from here:
Statisticians have devised several methods for detecting outliers. All the methods first quantify how far the outlier is from the other values. This can be the difference between the outlier and the mean of all points, the difference between the outlier and the mean of the remaining values, or the difference between the outlier and the next closest value. Next, standardize this value by dividing by some measure of scatter, such as the SD of all values, the SD of the remaining values, or the range of the data. Finally, compute a P value answering this question: If all the values were really sampled from a Gaussian population, what is the chance of randomly obtaining an outlier so far from the other values? If the P value is small, you conclude that the deviation of the outlier from the other values is statistically significant.
Google is your friend, you know. ;)
For your specific question of plotting, and your specific scenario of an average of 1-2 errors per day out of 150, the simplest thing might be to plot trimmed means, or the range of the middle 95% of values, or something like that. It really depends on what value you want out of the plot.
If you are really concerned with the true max and true of a day's prices, then you have to deal with the outliers as outliers, and properly exclude them, probably using one of the outlier tests previously proposed ( data point is x% more than next point, or the last n points, or more than 5 standard deviations away from the daily mean). Another approach is to view what happens after the outlier. If it is an outlier, then it will have a sharp upturn followed by a sharp downturn.
If however you care about overall trend, plotting daily trimmed mean, median, 5% and 95% percentiles will portray history well.
Choose your display methods and how much outlier detection you need to do based on the analysis question. If you care about medians or percentiles, they're probably irrelevant.