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 68.74% per annum.
- AMZN price at the close of May 20, 2024 was $183.54 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 55.72% per annum.
- AMZN price at the close of May 20, 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 AMZN 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: November 18, 2022
End date: May 20, 2024
a = 2.6318
b = 0.0014
s = 0.0536
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 68.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0536) – 1
= 23.91%
November 18, 2022 calculations
Top border of price channel:
Exp(Y883)
= Exp(a + b × X883 + 2 × s)
= Exp(a + b × 1,277 + 2 × s)
= Exp(2.6318 + 0.0014 × 1,277 + 2 × 0.0536)
= Exp(4.5694)
= $96.48
Bottom border of price channel:
Exp(Y883)
= Exp(a + b × X883 – 2 × s)
= Exp(a + b × 1,277 – 2 × s)
= Exp(2.6318 + 0.0014 × 1,277 – 2 × 0.0536)
= Exp(4.3550)
= $77.87
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.6318 + 0.0014 × 1,826 + 2 × 0.0536)
= Exp(5.3563)
= $211.93
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.6318 + 0.0014 × 1,826 – 2 × 0.0536)
= Exp(5.1419)
= $171.04
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 68.74% per annum.
- AMZN price at the close of May 20, 2024 was $183.54 and was inside the primary price channel.
Secondary Trend
Start date: May 6, 2024
End date: May 20, 2024
a = 9.2877
b = -0.0022
s = 0.0045
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0022) – 1
= -55.72%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0045) – 1
= 1.83%
May 6, 2024 calculations
Top border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 + 2 × s)
= Exp(a + b × 1,812 + 2 × s)
= Exp(9.2877 + -0.0022 × 1,812 + 2 × 0.0045)
= Exp(5.2526)
= $191.07
Bottom border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 – 2 × s)
= Exp(a + b × 1,812 – 2 × s)
= Exp(9.2877 + -0.0022 × 1,812 – 2 × 0.0045)
= Exp(5.2345)
= $187.63
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(9.2877 + -0.0022 × 1,826 + 2 × 0.0045)
= Exp(5.2214)
= $185.19
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(9.2877 + -0.0022 × 1,826 – 2 × 0.0045)
= Exp(5.2032)
= $181.86
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 55.72% per annum.
- AMZN price at the close of May 20, 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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