Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 63.45% per annum.
- EBAY price at the close of October 24, 2019 was $35.62 and was lower than the bottom border of the primary price channel by $6.20 (14.82%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 16.32% per annum.
- EBAY price at the close of October 24, 2019 was lower than the bottom border of the secondary price channel by $2.45 (6.43%). This indicates a possible reversal in the secondary trend direction.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of EBAY price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 19, 2018
End date: August 21, 2019
a = 1.3864
b = 0.0013
s = 0.0534
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 63.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0534) – 1
= 23.83%
October 19, 2018 calculations
Top border of price channel:
Exp(Y1,003)
= Exp(a + b × X1,003 + 2 × s)
= Exp(a + b × 1,453 + 2 × s)
= Exp(1.3864 + 0.0013 × 1,453 + 2 × 0.0534)
= Exp(3.4490)
= $31.47
Bottom border of price channel:
Exp(Y1,003)
= Exp(a + b × X1,003 – 2 × s)
= Exp(a + b × 1,453 – 2 × s)
= Exp(1.3864 + 0.0013 × 1,453 – 2 × 0.0534)
= Exp(3.2353)
= $25.41
August 21, 2019 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,759 + 2 × s)
= Exp(1.3864 + 0.0013 × 1,759 + 2 × 0.0534)
= Exp(3.8609)
= $47.51
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,759 – 2 × s)
= Exp(1.3864 + 0.0013 × 1,759 – 2 × 0.0534)
= Exp(3.6472)
= $38.37
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 63.45% per annum.
- EBAY price at the close of October 24, 2019 was $35.62 and was lower than the bottom border of the primary price channel by $6.20 (14.82%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 4, 2019
End date: October 23, 2019
a = 2.9447
b = 0.0004
s = 0.0302
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 16.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0302) – 1
= 12.84%
February 4, 2019 calculations
Top border of price channel:
Exp(Y1,074)
= Exp(a + b × X1,074 + 2 × s)
= Exp(a + b × 1,561 + 2 × s)
= Exp(2.9447 + 0.0004 × 1,561 + 2 × 0.0302)
= Exp(3.6516)
= $38.54
Bottom border of price channel:
Exp(Y1,074)
= Exp(a + b × X1,074 – 2 × s)
= Exp(a + b × 1,561 – 2 × s)
= Exp(2.9447 + 0.0004 × 1,561 – 2 × 0.0302)
= Exp(3.5308)
= $34.15
October 23, 2019 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(2.9447 + 0.0004 × 1,822 + 2 × 0.0302)
= Exp(3.7597)
= $42.94
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(2.9447 + 0.0004 × 1,822 – 2 × 0.0302)
= Exp(3.6389)
= $38.05
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 16.32% per annum.
- EBAY price at the close of October 24, 2019 was lower than the bottom border of the secondary price channel by $2.45 (6.43%). This indicates a possible reversal in the secondary trend direction.
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