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 15.15% per annum.
- PEP price at the close of April 26, 2024 was $175.58 and was higher than the top border of the primary price channel by $6.04 (3.57%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 8.69% per annum.
- PEP price at the close of April 26, 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 PEP 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 29, 2023
End date: March 15, 2024
a = 5.8908
b = -0.0005
s = 0.0316
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -15.15%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0316) – 1
= 13.49%
March 29, 2023 calculations
Top border of price channel:
Exp(Y987)
= Exp(a + b × X987 + 2 × s)
= Exp(a + b × 1,430 + 2 × s)
= Exp(5.8908 + -0.0005 × 1,430 + 2 × 0.0316)
= Exp(5.3104)
= $202.43
Bottom border of price channel:
Exp(Y987)
= Exp(a + b × X987 – 2 × s)
= Exp(a + b × 1,430 – 2 × s)
= Exp(5.8908 + -0.0005 × 1,430 – 2 × 0.0316)
= Exp(5.1838)
= $178.37
March 15, 2024 calculations
Top border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 + 2 × s)
= Exp(a + b × 1,782 + 2 × s)
= Exp(5.8908 + -0.0005 × 1,782 + 2 × 0.0316)
= Exp(5.1520)
= $172.77
Bottom border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 – 2 × s)
= Exp(a + b × 1,782 – 2 × s)
= Exp(5.8908 + -0.0005 × 1,782 – 2 × 0.0316)
= Exp(5.0254)
= $152.23
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 15.15% per annum.
- PEP price at the close of April 26, 2024 was $175.58 and was higher than the top border of the primary price channel by $6.04 (3.57%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 5, 2023
End date: April 26, 2024
a = 4.7286
b = 0.0002
s = 0.0179
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 8.69%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0179) – 1
= 7.42%
October 5, 2023 calculations
Top border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 + 2 × s)
= Exp(a + b × 1,620 + 2 × s)
= Exp(4.7286 + 0.0002 × 1,620 + 2 × 0.0179)
= Exp(5.1340)
= $169.70
Bottom border of price channel:
Exp(Y1,118)
= Exp(a + b × X1,118 – 2 × s)
= Exp(a + b × 1,620 – 2 × s)
= Exp(4.7286 + 0.0002 × 1,620 – 2 × 0.0179)
= Exp(5.0624)
= $157.98
April 26, 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(4.7286 + 0.0002 × 1,824 + 2 × 0.0179)
= Exp(5.1806)
= $177.78
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.7286 + 0.0002 × 1,824 – 2 × 0.0179)
= Exp(5.1090)
= $165.50
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 8.69% per annum.
- PEP price at the close of April 26, 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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