Time Series – Teaching for Understanding : Time Series – Teaching for Understanding By Nugzar Nachkebia*
&
Marina Alexander**
*Westmount School. Hawke’s Bay Campus. Hastings
**Woodford House, Havelock North
Time Series – Straightforward Problem : Time Series – Straightforward Problem Linear Component
L = m x + c
Seasonal Component
S = A sin(2 x / T)
Random Component
R = 2B RAND() generated by Excel
Total of the components above
T = L + S + R
Kay Parameters of the Model : Kay Parameters of the Model m – the gradient of the linear component
C – the original value of data
A – the amplitude of the seasonal component
T – the period of the seasonal component
B – the magnitude of the random component
No spikes
Specific learning outcomes : Specific learning outcomes How different components are contributing in the realistic time series?
The random component is masking the seasonal effect
Why we use moving means for finding a trend and a seasonal effect
Why is important to know the period of the seasonal effect?
How to find the period of a seasonal component?
Specific teaching outcomes : Specific teaching outcomes After these introductory lessens your students will be ready and keen to apply their knowledge to the real time series data and follow the standard traditional routines to learn the topic.
You will get easy method to design quality time series data for a practice or an assessment.
Excel in Action : Excel in Action The linear component
The Seasonal Component : The Seasonal Component
The Random Component : The Random Component
How the different components are contributing in the realistic time series? : How the different components are contributing in the realistic time series?
Finding the Period of the Seasonal Component : Finding the Period of the Seasonal Component Find the time interval between the local maxima 4 6 4 4 7
Find the time interval between the local minima : Find the time interval between the local minima 4 5 5 5 4
The period is: the most common number above or mean of the numbers : The period is: the most common number above or mean of the numbers 4 6 4 4 7 4 5 5 5 4
The moving mean technique : The moving mean technique Straight forward problem
Effect on a linear component
Effect on a seasonal component
Effect on a random component
Effect on a linear component : Effect on a linear component
Effect on a linear component(zoom in) : Effect on a linear component(zoom in)
Effect on a seasonal component : Effect on a seasonal component
Effect on a random component : Effect on a random component
What is the effect of the moving mean? : What is the effect of the moving mean? Linear component – None, if used odd order or too small if used even order.
Seasonal component – Removes completely, if used the correct order.
(The correct order = the period of the seasonal component)
Random component – Can not be removed completely. Moving mean reduces its amplitude only
Time Series Analysis : Time Series Analysis Find the most likely period of a seasonal component
Use the moving mean technique for finding a general trend (linear/nonlinear)
Find the individual seasonal component
Find the average seasonal effect
Make a prediction
Finding the Trend : Finding the Trend
Individual seasonal effect = row data - trend : Individual seasonal effect = row data - trend
Average seasonal effect = average of points with the same phase : Average seasonal effect = average of points with the same phase
Comparison of the model and the theory : Comparison of the model and the theory
Making a prediction : Making a prediction Trend line prediction + seasonal effect Seasonal effect Line prediction
Non Linear Models : Non Linear Models
Equation - Model : Equation - Model Price1 = 300*(1.05 + 0.01RAND())^t
Price2 =0.1* Price1*SIN(2pI()*t/7)
Price = Price1+Price2