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 23.64% per annum.
- HD price at the close of February 20, 2025 was $394.64 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.00% per annum.
- HD price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $3.19 (0.80%). 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 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: February 21, 2023
End date: February 20, 2025
a = 4.9655
b = 0.0006
s = 0.0541
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 23.64%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0541) – 1
= 24.18%
February 21, 2023 calculations
Top border of price channel:
Exp(Y755)
= Exp(a + b × X755 + 2 × s)
= Exp(a + b × 1,096 + 2 × s)
= Exp(4.9655 + 0.0006 × 1,096 + 2 × 0.0541)
= Exp(5.7111)
= $302.19
Bottom border of price channel:
Exp(Y755)
= Exp(a + b × X755 – 2 × s)
= Exp(a + b × 1,096 – 2 × s)
= Exp(4.9655 + 0.0006 × 1,096 – 2 × 0.0541)
= Exp(5.4945)
= $243.34
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.9655 + 0.0006 × 1,826 + 2 × 0.0541)
= Exp(6.1355)
= $461.97
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.9655 + 0.0006 × 1,826 – 2 × 0.0541)
= Exp(5.9189)
= $372.01
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 23.64% per annum.
- HD price at the close of February 20, 2025 was $394.64 and was inside the primary price channel.
Secondary Trend
Start date: April 15, 2024
End date: February 20, 2025
a = 4.4172
b = 0.0009
s = 0.0393
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.00%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0393) – 1
= 17.00%
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,515 + 2 × s)
= Exp(4.4172 + 0.0009 × 1,515 + 2 × 0.0393)
= Exp(5.8625)
= $351.59
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,515 – 2 × s)
= Exp(4.4172 + 0.0009 × 1,515 – 2 × 0.0393)
= Exp(5.7055)
= $300.50
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.4172 + 0.0009 × 1,826 + 2 × 0.0393)
= Exp(6.1430)
= $465.47
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.4172 + 0.0009 × 1,826 – 2 × 0.0393)
= Exp(5.9860)
= $397.83
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.00% per annum.
- HD price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $3.19 (0.80%). This indicates a possible reversal in the secondary trend direction.
- 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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