Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.88% per annum.
- HD price at the close of May 17, 2024 was $344.21 and was higher than the top border of the primary price channel by $2.94 (0.86%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.38% per annum.
- HD price at the close of May 17, 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: March 26, 2021
End date: December 1, 2023
a = 5.9170
b = -0.0001
s = 0.0829
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0829) – 1
= 39.32%
March 26, 2021 calculations
Top border of price channel:
Exp(Y467)
= Exp(a + b × X467 + 2 × s)
= Exp(a + b × 676 + 2 × s)
= Exp(5.9170 + -0.0001 × 676 + 2 × 0.0829)
= Exp(5.9901)
= $399.47
Bottom border of price channel:
Exp(Y467)
= Exp(a + b × X467 – 2 × s)
= Exp(a + b × 676 – 2 × s)
= Exp(5.9170 + -0.0001 × 676 – 2 × 0.0829)
= Exp(5.6585)
= $286.72
December 1, 2023 calculations
Top border of price channel:
Exp(Y1,143)
= Exp(a + b × X1,143 + 2 × s)
= Exp(a + b × 1,656 + 2 × s)
= Exp(5.9170 + -0.0001 × 1,656 + 2 × 0.0829)
= Exp(5.8557)
= $349.23
Bottom border of price channel:
Exp(Y1,143)
= Exp(a + b × X1,143 – 2 × s)
= Exp(a + b × 1,656 – 2 × s)
= Exp(5.9170 + -0.0001 × 1,656 – 2 × 0.0829)
= Exp(5.5241)
= $250.66
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.88% per annum.
- HD price at the close of May 17, 2024 was $344.21 and was higher than the top border of the primary price channel by $2.94 (0.86%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 5, 2022
End date: May 17, 2024
a = 5.3524
b = 0.0003
s = 0.0630
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.38%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0630) – 1
= 28.68%
May 5, 2022 calculations
Top border of price channel:
Exp(Y747)
= Exp(a + b × X747 + 2 × s)
= Exp(a + b × 1,081 + 2 × s)
= Exp(5.3524 + 0.0003 × 1,081 + 2 × 0.0630)
= Exp(5.7710)
= $320.85
Bottom border of price channel:
Exp(Y747)
= Exp(a + b × X747 – 2 × s)
= Exp(a + b × 1,081 – 2 × s)
= Exp(5.3524 + 0.0003 × 1,081 – 2 × 0.0630)
= Exp(5.5188)
= $249.34
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.3524 + 0.0003 × 1,824 + 2 × 0.0630)
= Exp(5.9720)
= $392.31
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.3524 + 0.0003 × 1,824 – 2 × 0.0630)
= Exp(5.7199)
= $304.86
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.38% per annum.
- HD price at the close of May 17, 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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