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 27.06% per annum.
- PFE price at the close of May 20, 2024 was $28.53 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.76% per annum.
- PFE price at the close of May 20, 2024 was higher than the top border of the secondary price channel by $1.84 (6.89%). 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 PFE 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 14, 2022
End date: May 14, 2024
a = 4.8320
b = -0.0009
s = 0.0618
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -27.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0618) – 1
= 28.05%
March 14, 2022 calculations
Top border of price channel:
Exp(Y709)
= Exp(a + b × X709 + 2 × s)
= Exp(a + b × 1,028 + 2 × s)
= Exp(4.8320 + -0.0009 × 1,028 + 2 × 0.0618)
= Exp(4.0668)
= $58.37
Bottom border of price channel:
Exp(Y709)
= Exp(a + b × X709 – 2 × s)
= Exp(a + b × 1,028 – 2 × s)
= Exp(4.8320 + -0.0009 × 1,028 – 2 × 0.0618)
= Exp(3.8195)
= $45.58
May 14, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(4.8320 + -0.0009 × 1,820 + 2 × 0.0618)
= Exp(3.3820)
= $29.43
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(4.8320 + -0.0009 × 1,820 – 2 × 0.0618)
= Exp(3.1347)
= $22.98
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 27.06% per annum.
- PFE price at the close of May 20, 2024 was $28.53 and was inside the primary price channel.
Secondary Trend
Start date: November 10, 2022
End date: May 14, 2024
a = 5.2555
b = -0.0011
s = 0.0448
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0448) – 1
= 19.61%
November 10, 2022 calculations
Top border of price channel:
Exp(Y877)
= Exp(a + b × X877 + 2 × s)
= Exp(a + b × 1,269 + 2 × s)
= Exp(5.2555 + -0.0011 × 1,269 + 2 × 0.0448)
= Exp(3.9129)
= $50.05
Bottom border of price channel:
Exp(Y877)
= Exp(a + b × X877 – 2 × s)
= Exp(a + b × 1,269 – 2 × s)
= Exp(5.2555 + -0.0011 × 1,269 – 2 × 0.0448)
= Exp(3.7339)
= $41.84
May 14, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,820 + 2 × s)
= Exp(5.2555 + -0.0011 × 1,820 + 2 × 0.0448)
= Exp(3.2911)
= $26.87
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,820 – 2 × s)
= Exp(5.2555 + -0.0011 × 1,820 – 2 × 0.0448)
= Exp(3.1120)
= $22.47
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 33.76% per annum.
- PFE price at the close of May 20, 2024 was higher than the top border of the secondary price channel by $1.84 (6.89%). 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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