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 65.30% per annum.
- HD price at the close of November 19, 2024 was $406.80 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 17.62% per annum.
- HD price at the close of November 19, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 HD 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: May 20, 2024
End date: November 19, 2024
a = 3.5186
b = 0.0014
s = 0.0284
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 65.30%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0284) – 1
= 12.02%
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,130)
= Exp(a + b × X1,130 + 2 × s)
= Exp(a + b × 1,643 + 2 × s)
= Exp(3.5186 + 0.0014 × 1,643 + 2 × 0.0284)
= Exp(5.8376)
= $342.97
Bottom border of price channel:
Exp(Y1,130)
= Exp(a + b × X1,130 – 2 × s)
= Exp(a + b × 1,643 – 2 × s)
= Exp(3.5186 + 0.0014 × 1,643 – 2 × 0.0284)
= Exp(5.7242)
= $306.18
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.5186 + 0.0014 × 1,826 + 2 × 0.0284)
= Exp(6.0896)
= $441.26
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.5186 + 0.0014 × 1,826 – 2 × 0.0284)
= Exp(5.9761)
= $393.92
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 65.30% per annum.
- HD price at the close of November 19, 2024 was $406.80 and was inside the primary price channel.
Secondary Trend
Start date: September 30, 2024
End date: November 19, 2024
a = 6.9620
b = -0.0005
s = 0.0175
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -17.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0175) – 1
= 7.23%
September 30, 2024 calculations
Top border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 + 2 × s)
= Exp(a + b × 1,776 + 2 × s)
= Exp(6.9620 + -0.0005 × 1,776 + 2 × 0.0175)
= Exp(6.0536)
= $425.62
Bottom border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 – 2 × s)
= Exp(a + b × 1,776 – 2 × s)
= Exp(6.9620 + -0.0005 × 1,776 – 2 × 0.0175)
= Exp(5.9837)
= $396.91
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.9620 + -0.0005 × 1,826 + 2 × 0.0175)
= Exp(6.0270)
= $414.47
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.9620 + -0.0005 × 1,826 – 2 × 0.0175)
= Exp(5.9572)
= $386.51
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 17.62% per annum.
- HD price at the close of November 19, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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