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 8.45% per annum.
- TSLA price at the close of May 17, 2024 was $177.46 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.34% per annum.
- TSLA price at the close of May 17, 2024 was inside the secondary price channel.
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 TSLA 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: December 4, 2020
End date: May 17, 2024
a = 5.7404
b = -0.0002
s = 0.2187
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -8.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.2187) – 1
= 139.84%
December 4, 2020 calculations
Top border of price channel:
Exp(Y391)
= Exp(a + b × X391 + 2 × s)
= Exp(a + b × 564 + 2 × s)
= Exp(5.7404 + -0.0002 × 564 + 2 × 0.2187)
= Exp(6.0414)
= $420.47
Bottom border of price channel:
Exp(Y391)
= Exp(a + b × X391 – 2 × s)
= Exp(a + b × 564 – 2 × s)
= Exp(5.7404 + -0.0002 × 564 – 2 × 0.2187)
= Exp(5.1666)
= $175.31
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(5.7404 + -0.0002 × 1,824 + 2 × 0.2187)
= Exp(5.7365)
= $309.99
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.7404 + -0.0002 × 1,824 – 2 × 0.2187)
= Exp(4.8617)
= $129.25
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 8.45% per annum.
- TSLA price at the close of May 17, 2024 was $177.46 and was inside the primary price channel.
Secondary Trend
Start date: June 29, 2023
End date: May 17, 2024
a = 8.0538
b = -0.0016
s = 0.0837
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0837) – 1
= 39.77%
June 29, 2023 calculations
Top border of price channel:
Exp(Y1,035)
= Exp(a + b × X1,035 + 2 × s)
= Exp(a + b × 1,501 + 2 × s)
= Exp(8.0538 + -0.0016 × 1,501 + 2 × 0.0837)
= Exp(5.8119)
= $334.27
Bottom border of price channel:
Exp(Y1,035)
= Exp(a + b × X1,035 – 2 × s)
= Exp(a + b × 1,501 – 2 × s)
= Exp(8.0538 + -0.0016 × 1,501 – 2 × 0.0837)
= Exp(5.4771)
= $239.15
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(8.0538 + -0.0016 × 1,824 + 2 × 0.0837)
= Exp(5.2935)
= $199.04
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(8.0538 + -0.0016 × 1,824 – 2 × 0.0837)
= Exp(4.9586)
= $142.40
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.34% per annum.
- TSLA 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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